WBBSE Solutions For Class 10 Physical Science And Environment Chapter 4 Phenomena Of Heat

Chapter 4 Phenomena Of Heat Topic A Thermal Expansion of Solid, Liquid and Gas Synopsis:

1. If the temperature of a solid substance is increased, its area and volume also expand: This phenomenon is called the thermal expansion of a solid substance.

2. Thermal expansion of a solid is of three types:
(1)Expansion of length
(2)Expansion of area
(3)Expansion of volume.

3. The coefficient of linear expansion of a solid is the fractional increase in its length per degree rise in temperature. It is generally denoted by or. If l₁ and l₂  are the lengths of a solid substance (say a metallic rod) at temperatures t₁ and t₂ respectively, then \(\alpha=\frac{l_2-l_1}{l_1\left(t_2-t_1\right)}\)

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4. Unit of coefficient of surface expansion, \(=\frac{\text { unit of length }}{\text { unit of length } \times \text { unit of temperature }}\),\(=\frac{1}{\text { unit of temperature }}\)

Therefore, unit of a is independent of unit of length and it depends on the unit of temperature. So, CGS unit of α is °C^-1 , in SI it is K^-1 and in FPS system its unit is °F^-1.

5. The change in temperature by 1°F = 5/9°C change in temperature.
∴ value of α in Fahrenheit scale (α_F) = 5/9 X value of or in Celsius scale (α_c).

6. The change in temperature by 1K = 1°C change in temperature
∴ Value α in Kelvin ( α_k) = value of α in Celsius scale (α_c).
i..e., α_k=α_c= 9/5α_F

7. The coefficient of surface expansion of a solid is the fractional increase in its surface area per degree rise in temperature. It is generally denoted by β. If S₁ and S₂ are the surface areas of a solid at temperatures t₁ and t₂ respectively, then \(\beta=\frac{S_2-S_1}{S_1\left(t_2-t_1\right)}\).

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8. Unit of coefficient of surface expansion \(=\frac{\text { unit of area }}{\text { unit of area } \times \text { unit of temperature }}\) , \(=\frac{1}{\text { unit of temperature }}\)

Unit in CGS system is °C^-1  , in SI it is K^-1, and in FPS system it’s unit is °F^-1 .

9. The coefficient of volume expansion of a solid is the fractional increase in its volume per degree rise in temperature. It is usually denoted by γ. if V₁ and V₂ are the volumes of a solid at t₁ and t₂ respectively, then coefficient of volume expansion, \(\gamma=\frac{V_2-V_1}{V_1\left(t_2-t_1\right)}\)

10. Unit of coefficient of volume expansion γ, \(=\frac{\text { unit of volume }}{\text { unit of volume } Χ \text { unit of temperature }}\) = \(=\frac{1}{\text { unit of temperature }}\)

Unitin CGS system is °C^-1  , in SI it is K^-1, and in FPS system its unit is °F^-1.

10. Relation among α, β and γ is α = β/2 = γ/2

11. ln case of a liquid kept in a vessel, if the expansion of the vessel is neglected, the expansion of the liquid that is obtained is the apparent expansion of the liquid. In the case of the same liquid kept in a vessel, if the expansion of the vessel is taken into consideration along with the apparent expansion of the liquid, then the expansion of the liquid is called the real expansion of the liquid.

12. The coefficient of real expansion of a liquid is the ratio of actual expansion in volume to its original volume for each degree rise in temperature.

13. The coefficient of apparent expansion of a liquid is the ratio of apparent expansion in volume to its original volume for each degree of rise in temperature. The relation between the coefficients of real and apparent expansions of a liquid is given by γ_r = γ_a + γ_g

where γ_r and γ_a are the respective, coefficients of real and apparent expansions of the liquid and γ_g is the coefficient of volume expansion of the substance of the vessel in which the liquid is kept.

14. The units of coefficient of apparent or real expansion of a liquid depend only on the unit of temperature and not on the unit of volume. The unit of each is °C^-1  or °F^-1 or K^-1  and the dimensional coefficient is Θ^-1.

15. By keeping the pressure on a definite mass of gas constant, if the temperature is raised from 0°C to 1°C, then the ratio of expansion in volume to the initial volume of a gas is called coefficient of volume expansion of that gas and it is expressed as γ_p.

Suppose, V₀ and V_t are the respective volumes of a definite mass of gas at 0°C and t°C at constant pressure. Then we can write, \(\gamma_p=\frac{V_t-V_0}{V_t t} \text { or, } V_t=V_0\left(1+\gamma_p t\right)\).

16. Coefficient of volume expansion of an ideal gas, \(\gamma_p=\frac{1}{273}{ }^{\circ} \mathrm{C}^{-1}\)

Chapter 4 Phenomena Of Heat Topic A Thermal Expansion of Solid, Liquid and Gas Short And Long Answer Type Questions:

Question 1. What is the thermal expansion of a solid substance? There are two scales for measurement of length (distance). One is made of invar and the other of iron. Which one of these two is more suitable for measuring accurately the distance between two definite places in different times of the year Give a reason for your answer.

Answer:

The thermal expansion of a solid substance

1. If the temperature of a solid substance is increased, the volume of the substance expands. This expansion due to the increase of temperature is called the thermal expansion of a solid substance.

2. The temperature of a place is different during different seasons of the year. The distance between two places does not depend on the temperature. But if the measuring scale is made of a metal, the length of the scale changes according to the temperature. As a result, different readings are found for the same length at different times of the year with this scale.

3. Invar has a coefficient of linear expansion (1.2 x 10^-6K^-1 at 20°C) which is much lower than the coefficient of linear expansion of iron (11.8 x 10^-6K^-1 at 20°C). This means that the change in length of a scale made of invar is insignificant compared to the change in length of an equal scale made of iron. For this reason, a scale made of invar is more suitable for the measurement of distance.

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Question 2. Write the expression for the coefficient of linear expansion of a solid. What do you mean by the statement that the coefficient of linear expansion of iron is 12 x 10^-6/°C?

Answer:
1. Suppose l₁ is the length of a solid substance at temperature t₁ and the length becomes l₂  when the temperature is raised to t₂ . If α is the coefficient of linear expansion of the solid substance, then according to the definition, \(\alpha=\frac{l_2-l_1}{l_1\left(t_2-t_1\right)}\)

The above statement means that if the temperature, of an iron rod is increased by 1°C, 12 x 10^-6 part of its original length increases.

Question 3. There are several rods of same length and made of the same substance. What is the change in their lengths for a different increase in their temperatures? Show that: the unit of coefficient of linear expansion does not depend on the unit of length but depends only on the unit of temperature.

Answer:
1. The change in lengths of the rods made of the same substance and having the same length is directly proportional to the change in temperature. Therefore more the temperature is increased, the more is the change in length of the rod. The ratio between the change in temperature and the change in this length is constant.

Mathematically, change in length ex-change in temperature or, (l₁-l₂) ∝ (t₂ -t₁)

2. Suppose, l₁ is the 1ength of a rod at temperature t_1. It is heated to a higher temperature t₂ when its length becomes l₂. Hence, the coefficient of linear expansion,

∴ \(\alpha=\frac{l_2-l_1}{l_1\left(t_2-t_1\right)}\)

\(\frac{l_2-l_1}{l_1}\) is the ratio of two quantities having the same dimension. So it has no unit. Therefore, the coefficient of linear expansion depends only on the unit of (t₂  t₁), i.e., on the unit of temperature.

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Question 4. There are several rods of different, lengths made of the same substance. If the temperature of the rods Is increased by the same amount, what is the change in their lengths? A stopper made of steel gets stuck firmly in the mouth of a bottle made of brass. How can you open it?

Answer:
1. The change in length of the rods made of the same substance and of different lengths is directly proportional to the lengths of the rods for the same increase of temperature, in other words, more the initial length of the rod, more is the change of length of the rod. The ratio between the initial length and the change in length is constant.

∴ Mathematically, change in length ∝ initial length or, (l₁-l₂) ∝ l₁

2. The coefficient of linear expansion for brass is greater than that for steel. If the system is heated, the expansion of brass is more than that of steel. As a result, the stopper is stuck all the more. But if the system is cooled, the contraction of brass is more than that of iron. Hence, the stopper loosens and comes out.

Question 5. How does the length of a rod depend on the initial length of the expanding rod (l₂) and on difference of temperature (Δt)? Establish a relationship between the coefficients of linear expansion in the Celcius and Fahrenheit scales.

Answer: Expansion of length (Δl) is directly proportional to the initial length of the rod and increase in temperature (Δt), i.e. Δl ∝Δl₁ [when Δt remains the same] and Δl ∝ Δt [when l₁ is constant]
∴ Δl ∝ l₁Δt[when both l₁ and Δt change]

Let us assume that the coefficient of linear expansion of a solid substance, α = x/°C.
Again, we know that, change by 1°C = change by 9/5°F

\(\alpha=\frac{x}{\frac{9}{5} \circ \mathrm{F}}=\frac{5}{9} x /{ }^{\circ} \mathrm{F}\)

Hence, if the coefficients of linear expansion are α_c and α_F respectively, then = α_F 5/9 α_c.

Question 6. Explain what happens when a bimetallic strip made of brass and iron is heated.

Answer: For the same increase in temperature, different solid substances of the same length have different amount of expansion. The coefficient of linear expansion of brass is more than that of iron. The lengths of brass and iron are the same in the bimetallic strip. As the linear expansion of brass is more than that of iron for the same rise in temperature, the bi-metallic strip bends with brass remaining outside.

Question 7. There Is one rod of iron, one iron scale and one invar scale in a room. The temperature of the room changes every hour. By which scale, the length of the rod is to be measured so that no change of length is observed? Establish the condition to maintain a constant difference in the lengths of two rods at all temperatures.

Answer: For the same change in temperature, change in length of invar is negligible compared to the change in length of iron which is much more. As the rod is made of iron, its change in length per unit length is equal to the change in length per unit length of the scale, with the same change in temperature. As a result, no change in length of the rod is noticed if the length of rod is measured with the iron scale.

Let us assume that at temperature t_1, lengths of the two rods are l₁ and l₂ ( l₁ > l₂ ). After the temperature increases to t₂, the lengths of these two rods become l’₁  and l’₂ respectively. Let the coefficients of linear expansion of these rods be α₁ and α₂ respectively.

According to the given condition,

\(l_1-l_2=l_1^{\prime}-l_2^{\prime}\) or, \(l_1^{\prime}-l_1=l_2^{\prime}-l_2\)

or, \(l_1 \alpha_1\left(t_2-t_1\right)=l_2 \alpha_2\left(t_2-t_1\right)\)

or, \(l_1 \alpha_1=l_2 \alpha_2\) or, \(\frac{l_1}{l_2}=\frac{\alpha_2}{\alpha_1}\)

This is the required condition.

Wbbse Class 10 Physical Science And Environment

Question 8. An iron rod is fixed along the diameter of a circular iron ring. If the system is heated uniformly, does the ring remain circular? Explain.

Answer:

Given

An iron rod is fixed along the diameter of a circular iron ring. If the system is heated uniformly,

Suppose, the length of the iron rod, is l₁ =1.
Let the length of the iron ring be l₂.
So, the diameter of the circle = l and the length of the iron ring, l₂ = πl

∴\(\frac{l_2}{l_1}=\frac{\pi l}{l}=\pi\)

Suppose, increase in temperature of the system = t
Now, the length of the iron rod, l’₁  = l(1+ αt) [where a is the coefficient of linear expansion of iron] and length in the iron] and length in the iron ring l’₂ = πl(1 +αt)

∴ \( \frac{l_2^{\prime}}{l_1^{\prime}}=\frac{\pi l(l+\alpha t)}{l(l+\alpha t)}=\pi\)

As the ratio of the circumference of the circle and diameter remain the same in both cases, the ring remains circular.

Question 9. Write the expression for the coefficient of surface expansion for solid. Show that the unit of coefficient of area expansion does not depend on the unit of area but only on the unit of temperature.

Answer: Let the coefficient of surface expansion be denoted by β.

If S₁ and S₂ are the surface areas of a solid at temperatures t₁ and t₂  respectively, then the increase in surface area is (S₂ – S₁) with a rise in temperature of ( t₂ – t₁).

∴ \(\beta=\frac{S_2-S_1}{S_1\left(t_2-t_1\right)}\)

Here \(\frac{\left(S_2-S_1\right)}{S_1}\) is a ratio of two similar quantities and thus does not have any unit. Therefore, the unit of coefficient of surface expansion depends only on the unit of ( t₂ – t₁) i.e., on the unit of temperature.

Wbbse Class 10 Physical Science Chapter 4 Question Answer

Question 10. On which factors and how does the surface expansion of a solid depend? Why is some gap left between two iron plates in a joint of a bridge?

Answer: Suppose, the surface area of a solid is S₁ at temperature t₁. If the temperature is increased to t₂, the area becomes S₂ .
Thus, expansion of area = (S₂ – S₁) and increase of temperature = (t₂ – t₁).

Therefore, the expansion of area is directly proportional to the initial area of the solid and also on the increase in temperature.
∴ (S₂ – S₁) α S₁ [when (t₂ – t₁) remains the same] and (S₂ – S₁) ∝ (t₂ – t₁) [when S₁ is constant]
i.e., S₂ – S₁ ∝ t₂ – t₁ [when both S₁  and (t₂ – t₁) are changing]

A solid get expansion due to an increase of temperature. The iron plates of the joints of a bridge are heated by the sun’s rays and require sufficient space for expansion. For this reason, some gap is left between the two plates. Without this gap, one iron plate puts pressure on another due to thermal expansion. As a result, the bridge may get damaged.

Question 11. Write down the expression for the coefficient of volume expansion of solid. Show that the unit of coefficient of volume expansion does not depend on the unit of volume but depends only on the unit of temperature.

Answer:
1. Let the expression be denoted by γ. If V₁ and V₂ are the volumes of a solid at temperatures t₁ and t₂ respectively, then the increase in volume is (V₂ – V₁) with a rise in temperature of (t₂ – t₁).

∴\(\gamma=\frac{V_2-V_1}{V_1\left(t_2-t_1\right)}\)

\(\gamma=\frac{\text { increase in volume }}{\text { initial volume } \times \text { increase in temperature }}\)

 

Therefore, unit of coefficient of volume expansion \(=\frac{\text { unit of volume }}{\text { unit of volume } \times \text { unit of temperature }}\) = \(=\frac{1}{\text { unit of temperature }}\)

Hence, unit of coefficient of volume expansion depends only on the unit of temperature.

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Question 12. What do you mean by the statement that the coefficient of volume expansion of iron is 36 x 10^-6/°C? A roof casting generally needs rods of iron but not of any other metal explain why?

Answer:
1. The coefficient of volume expansion of iron is 36 x 10^-6/°C means that with a rise of temperature of 1°C, the volume increases by 36 x 10^-6 of its initial volume.

Alternative answer: The coefficient of volume expansion of iron is 36 x 10^-6/°C. Thus, if the temperature of 1cm³ or 1m³ of iron is increased by 1°C, the volume of iron increases by  36 x 10^-6cm³ or 36 x 10^-6m³.

2. During casting, iron rods are entered into concrete. In summer, temperature is high and so both concrete and rod undergo thermal expansion. On the other hand, temperature is low in winter and both of them contract. It has been found that the coefficient of expansion for both are almost equal. That is why only iron rods are used during casting. Expansion or compression of any other metal does not match with that *of concrete and as a result, cracks develop in the casting.

Question 13. Two Identical sheets, one of copper and the other of iron, are riveted together. What happens if this system is heated? What happens if the temperature of this system is decreased?

Answer:

Given

Two Identical sheets, one of copper and the other of iron, are riveted together.

The coefficient of linear expansion of copper is greater than that of iron. So, with the same increase in temperature, linear expansion of copper is more than that of iron. As the two sheets are riveted together, this pair of sheets bend. Expansion of copper being more, it remains outside.

With the decrease in temperature, this pair of sheets bend. Contraction of copper being more, it remains inside copper.

Question 14. Establish the relation between apparent and real expansions of a liquid with the help of a simple experiment.

Answer:
Experiment: At first, a glass flask fitted with a stopper is taken. A thin glass tube is entered through the stopper and a scale is fixed with the tube. A portion of the tube and the entire glass flask are filled with a coloured liquid. Let the initial level of liquid in the tube be A.

Now this flask is immersed in a vessel filled with hot water. It can be observed that the level of liquid comes down from A to B. Then the level of liquid goes up slowly to C.

Conclusion: When the flask is immersed in hot water, glass gathers heat from water and expands itself. This is the reason why the level of liquid in the tube comes down from A to B. Then heat is transmitted to liquid through glass and liquid expands so that its level in the tube goes up.

From this experiment, it is clearly understood that the volume of the liquid in the glass tube between points A and B is the measure of expansion of the vessel and the volume of the liquid in the glass tube between points, S and C is the measure of real expansion of the liquid. If we ignore the expansion of the vessel, the expansion of the liquid is called apparent expansion.

Therefore, the volume of the liquid in the glass tube between points A and C represents the apparent expansion of liquid.
Here, BC = AB+AC
Hence, real expansion of the liquid = expansion of volume of the vessel + apparent expansion of the liquid.

Question 15. What is the coefficient of apparent expansion of a liquid? What are the factors on which the apparent expansion of a liquid depends?

Answer: The coefficient of apparent expansion of a liquid is the ratio of apparent expansion in volume to its original volume for each degree rise in temperature.

The apparent expansion of a liquid depends on the following factors:
1. Initial volume of the liquid
2. Increase of temperature
3. Nature of the liquid
4. Substance of the vessel.

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Question 16. Write the expression for the coefficient of apparent expansion of a liquid. A right circular cylinder contains liquid. If the cylinder is heated, the level of liquid in it remains unchanged. How is it possible?

Answer:
1. Suppose, the volume of a definite mass of a liquid is V₁ at temperature t₁ and if the temperature is increased to t₂, its apparent volume is V₂.

Therefore, coefficient of real expansion of the liquid \(\gamma_r=\frac{V_2-V_1}{V_1\left(t_2-t_1\right)}\)

2. Unit of the coefficient of real expansion of a liquid is °C^-1  or °F^-1 or K^-1  .

Question 17. What is the coefficient of real expansion of a liquid? What are the factors on which the real expansion of a liquid depends?

Answer:

1. The coefficient of real expansion of a liquid is the ratio of actual expansion in volume to its original volume for each degree rise in temperature.

2. The real expansion of a liquid depends on the following factors:
(1)Initial volume of the liquid 0 Increase in temperature
(2)Nature of the liquid.

Question 18. Between the coefficients of apparent and real expansions, which does measure the inherent property of a liquid?

Answer:

1. To measure the coefficient of thermal expansion of a liquid, it must be kept in a vessel. The coefficient of apparent expansion of a liquid depends on the coefficient of volume expansion of the vessel.

2. For different vessels made of different substances, coefficients of apparent expansion are different; but the coefficient of real expansion remains unchanged. Therefore, between the coefficients of apparent and real expansions, coefficient of real expansion measures the inherent property of a liquid.

Question 19. Write the expression for the coefficient of apparent expansion of a liquid. A right circular cylinder contains liquid. If the cylinder is heated, the level of liquid in it remains unchanged. How is it possible?

Answer:

Suppose, the volume of a definite mass of a liquid is V₁ at temperature t₁ and if the temperature is increased to t₂, its apparent volume is V’₂.

Therefore, coefficient of apparent expansion of the liquid, γ_a = \(\gamma_a=\frac{V_2^{\prime}-V_1}{V_1\left(t_2-t_1\right)}\)

If the cylinder and the liquid equally expand for a increase in temperature, no change occurs in the level of liquid in the cylinder. In this case, the coefficient of apparent expansion of the liquid is zero.

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Question 20. Write the expression for coefficient of volume expansion of a gas and calculate its value with the help of Charles’ law.

Answer:

Suppose, the volume of a definite mass of gas at 0°C is V/Q. Under constant pressure if the temperature is increased to t°C, the volume becomes Vt.

By definition of coefficient of volume expansion, we may write \(\gamma_p=\frac{V_t-V_0}{V_0 t}\) ……(1)

From equation (1), we get, V_t – V₀ =V₀ γ_pt or, V_t=V₀+γ_pt or, V_t= V₀(l + γ_pt)
Again, we get from Charles’ law, \(V_t=V_0\left(1+\frac{t}{273}\right)\) …..(3)

By comparing equations (2) and (3), we get the value of coefficient of volume expansion of a gas as \(\gamma_p=\frac{1}{273}{ }^{\circ} \mathrm{C}^{-1}=3.663 \times 10^{-3 \circ} \mathrm{C}^{-1}\).

Question 21. What do you mean by apparent expansion and real expansion of liquid? A liquid has coefficient of apparent expansion but in case of a gas, why is the coefficient of apparent expansion not taken into consideration?

Answer:

Apparent expansion of liquid: In case of a liquid kept in a vessel, if the expansion of the vessel is neglected, the expansion of the liquid that is obtained is called the apparent expansion of the liquid.

Real expansion of liquid: In case of a liquid kept in a vessel, if the expansion of the vessel is taken into consideration along with the apparent expansion of the liquid, the expansion of the liquid is called the real expansion of the liquid.

Both liquid and gaseous substances have to be kept inside a vessel and then heated. As a result, expansion of the vessel also takes place along with the expansion of liquid or gas. Expansion of solid is less than the expansion of liquid but, it cannot be neglected. But in case of a gas, expansion of the vessel is not considered as the expansion of solid is 1/100th part of the expansion of a gas taken in it. For this reason, coefficient of apparent expansion of gas is not taken into account.

Chapter 4 Phenomena Of Heat Topic A Thermal Expansion of Solid, Liquid and Gas Very Short Answer Type Questions:

Question 1. Unit of coefficient of surface expansion depends
1. Only on the unit of area
2. Only on the unit of temperature
3. On the units of area and temperature
4. On the units of temperature and time

Answer: 2. Only on the unit of temperature

Question 2. Dimensional formula of coefficient of volume expansion is
1. L³ Θ^-1  
2.Θ^-2
3. LΘ^-1 
4. Θ^-1

Answer: 4. Θ^-1

Question 3. The value of the coefficient of volume expansion of gas is
1. 1/273 °C^-1 
2. 2/273 °C^-1 
3. 4/273 °C^-1 
4. 1/91 °C^-1 

Answer:1. 1/273 °C^-1 

Question 4. The initial temperature at the time of expansion of gas is taken as
1. Any temperature
2. 0K
3. 0°C
4. 4°C

Answer: 3. 0°C

Question 5. Which of the following liquids displays anomalous expansion?
1. Mercury
2. Kerosene
3. Glycerine
4. Water

Answer: 4. Water

Question 6. Expansion of the length of a solid depends on
1. Initial length
2. Increase in temperature
3. The material
4. All of the above

Answer: 4. All of the above

Question 7. If the coefficient of linear expansion of a solid substance is 27xlO-6/°C, what is the value in Fahrenheit scale?
1. 12 x 10^-6°F^-1
2. 16 X 10^-6°F^-1
3. 15 X 10^-6°F^-1
4. 18 X 10^-6°F^-1

Answer:  3. 15 X 10^-6°F^-1

Question 8. Which of the following has practically no expansion in spite of increase in temperature?
1. Iron
2. Nickel
3. Steel
4. Invar (nickel-iron alloy)

Answer: 4. Invar (nickel-iron alloy)

Question 9. If α, β and γ are the coefficients of linear expansion, surface expansion and volume expansion of a solid substance respectively, then
1. α has the highest value
2. β has the highest value
3. γ has the highest value
4. α, (β and γ have equal values

Answer: 3. γ has the highest value

Question 10. If the lengths of a solid substance with α as the coefficient of linear expansion are l₁ and l₂ at temperatures. t₁ and t₂ respectively (where t₂ > t₁ ), then
1. \(\alpha=\frac{l_2-l_1}{t_2-t_1}\)
2. \(\alpha=\frac{l_1}{\left(l_2-l_1\right)\left(t_2-t_1\right)}\)
3. \(\alpha=\frac{\left(l_2-l_1\right)^2}{l_1\left(t_2-t_1\right)}\)
4. \(\alpha=\frac{l_2-l_1}{l_1\left(t_2-t_1\right)}\)

Answer: 4. \(\alpha=\frac{l_2-l_1}{l_1\left(t_2-t_1\right)}\)

Question 11. If the surface areas of a solid substance with β as the coefficient of surface expansion are S₁ and S₂ at temperatures t₁ and t₂ respectively (where t₂ > t₁ ), then
1. \(\beta=\frac{S_2-S_1}{t_2-t_1}\)
2. \(\beta=\frac{S_2}{\left(S_2-S_1\right)\left(t_2-t_1\right)}\)
3. \(\beta=\frac{S_2-S_1}{S_1\left(t_2-t_1\right)}\)
4. \(\beta=\frac{S_2}{S_1\left(t_2-t_1\right)}\)

Answer: 3. \(\beta=\frac{S_2-S_1}{S_1\left(t_2-t_1\right)}\)

Question 12. If the volumes of a solid substance with γ as the coefficient of volume expansion are V₁ and V₂ at temperatures and t₂ respectively (where t₂ > t₁), then
1. \(\gamma=\frac{V_2-V_1}{V_1\left(t_2-t_1\right)}\)
2. \(\gamma=\frac{V_2-V_1}{t_2-t_1}\)
3. \(\gamma=\frac{V_2\left(t_2-t_1\right)}{\left(V_2-V_1\right)}\)
4. \(\gamma=\frac{V_1\left(t_2-t_1\right)}{\left(V_2-V_1\right)}\)

Answer:1. \(\gamma=\frac{V_2-V_1}{V_1\left(t_2-t_1\right)}\)

Question 13. If the temperature of a metallic rod of length 4 m is increased by 2°C, its length increases by 88 x 10^-6m . α of this rod is
1. 9 x 10^-6 °C^-1 
2. 10 x 10^-6 °C^-1
3. 11 X 10^-6 °C^-1
4. 12 x 10^-6 °C^-1

Wbbse Class 10 Physical Science Solutions

Answer: 3. 11 X 10^-6 °C^-1

Question 14. If the coefficients of linear expansion of a solid substance are ac and aF in Celcius and Fahrenheit scales respectively, then
1. α_F = 5/9 α_c
2. α_F = 9/5 α_c
3. α_F = 5/8 α_c
4. α_F = 5/6 α_c

Answer: 1. α_F = 5/9 α_c

Question 15. The temperatures of two iron rods of lengths 1 m and 2 m are increased to the same extent. What is the ratio of expansion of their lengths?
1. 1:2
2. 1:4
3. 1:8
4. 2:1

Answer: 1. 1:2

Question 16. If any solid substance is heated, which parameter is extended?
1. Only length
2. Only area
3. Only volume
4. All the three

Answer: 4. All the three

Question 17. There are two rods made of the same substance, each of length l. But their radii are r and 2 r, respectively. If the temperatures of both the rods are increased by the same amount, then
1. The length of the first rod increases more
2. The length of the second rod increases more
3. Both increase by the same length
4. It is not possible to predict their expansion

Answer: 3. Both increase by the same length

Question 18. There is a hole in the middle of a metal sheet. What happens if the temperature is increased?
1. Radius of the hole decreases
2. Radius of the hole increases
3. Radius of the hole remains unchanged
4. It is not possible to say whether the radius of the hole will increase or decrease

Answer: 2. Radius of the hole increases

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Question 19. There are two spheres made of the same substance and having the same radii, one is solid but the other is hollow. If the temperature of both the spheres is increased by the same amount, then
1. Expansion of the hollow sphere is more
2. Expansion of the solid sphere is more
3. Both have the same expansion
4. It is not possible to say which sphere will have more expansion

Answer: 3. Both have the same expansion

Question 20. There are two holes of radii r₁ and r₂ (r_{1 >} r₂) inside a metallic plate. If the metallic plate is heated
1. Value of r₁ increases, value of r2 decreases
2. Values of both r₁ and r₂ increase
3. Values of both r₁ and r₂ decrease
4. value of r₁ decreases, value of r₂ increases

Answer: 2. Values of both r₁ and r₂ increase

Question 21. A metallic rod is attached along the diameter of a circular metal plate. Both are made of the same element. If the system is heated, the ratio of the circumference and the diameter of the circle is
1. π
2. π/2
3. π/4
4. π/6

Answer: 1. π

Question 22. The dimension of the coefficient of surface expansion of a solid is
1. 1 in length, 2 in mass, 1 in temperature
2. 1 in length, 2 in time, 1 in temperature
3. -1 in temperature
4. 2 in temperature

Answer: 3. -1 in temperature

Question 23. The dimension of the coefficient of volume expansion of a solid is
1. 2 in length, 1 in temperature
2. 2 in mass, 1 in temperature
3. 1 in length, 1 in temperature
4. -1 in temperature

Answer: 4. -1 in temperature

Wbbse Class 10 Physical Science Solutions

Question 24. Volume expansion of a solid depends
1. Only on the initial volume
2. Only on the rise of temperature
3. Only on the coefficient of volume expansion
4. On all the above

Answer: 4. On all the above

Question 25. Surface expansion of a solid depends
1. Only on the initial surface area
2. Only on the rise of temperature
3. Only on the coefficient of surface expansion
4. On all the above

Answer: 4. On all the above

Question 26. For accurate measurement during expansion of a liquid, initial temperature is taken as
1. 0°c
2. 0K
3. 4°c
4. 10°c

Answer: 1. 0°c

Question 27. If the thermal conductivity of glass, k = 0.0025 cal •cm^-1 • °C^-1  • s^-1, then its value in SI is
1. 1.05 W • m^-1 • K^-1
2. 1.1 W • m • K^-1
3. 1 W • m^-1• K^-1
4. 1.2 W • m^-1 • K^-1

Answer: 1. 1.05 W • m^-1 • K^-1

Question 28. If the temperatures on the two sides of a heated rod are the same, then the value of thermal conductivity of the rod (in the unit cal •cm^-1 • °C^-1  • s^-1) is
1. 1
2. 0.5
3. 1000
4. ∞

Answer: 4. ∞

Question 29. There are two rods A and B of lengths lt and l2, and coefficients of linear expansion a± and az, respectively. What is the condition for the difference between the two lengths to remain unchanged at any temperature?
1. \(I_1 \alpha_1^2=I_2 \alpha_2^2\)
2. \(l_1^2 \alpha_1=I_2^2 \alpha_2\)
3. \(I_1 \alpha_2=I_2 \alpha_1\)
4. \(I_1 \alpha_1=I_2 \alpha_2\)

Answer: 4. \(I_1 \alpha_1=I_2 \alpha_2\)

Question 30. The volume of an iron sphere is 1000 cm3. What is the new volume of the sphere if the temperature is increased by 4°C? 7 for iron = 36 x lO-6^-1.
1. 0.15 cm³
2. 0.144 cm³
3. 0.154 cm³
4. 0.16 cm³

Answer: 2. 0.144 cm³

Question 31. When an aluminium ball is heated, the largest percentage increase will occur in its
1. Diameter
2. Area
3. Volume
4. Density

Answer: 3. Volume

Question 32. A bar of iron is 100 cm long at 20°C. At 19°C it will be (a of iron = 11 x 10^-6 /°C)
1. 11 x 10^-5 cm longer
2. 11 x 10^-6 cm shorter
3. 11 x 10^-4 cm shorter
4. 11 x 10^-4 cm longer

Answer: 3. 11 x 10^-4 cm shorter

Question 33. A solid ball of metal has a concentric spherical cavity within it. If the ball is heated, the volume of a cavity will
1. Increase
2. Decrease
3. Remain unaltered
4. First increases then decreases

Answer: 1. Increase

Question 34. When a bimetallic strip is heated, it
1. Does not bend at all
2. Get twisted in the form of a helix
3. Bends in the form of an arc with the more expandable metal outside
4. Bend in the form of an arc with the more expandable metal inside

Answer: 3. Bends in the form of an arc with the more expandable metal outside

Question 35. The coefficient of superficial expansion of a solid is 2×10^-5/°C- It’s coefficient of linear expansion is
1. 4 x 10^-5/°C
2. 3 x 10^-5/°C
3. 2 x 10^-5/°C
4. 1 x 10^-5/°c

Answer: 4. 1 x 10^-5/°c

Question 36. If the length of a cylinder on heating increases by 2%. The area of the base will increase by
1. 0.5%
2. 2%
3. 1%
4. 4%

Answer: 4. 4%

Chapter 4 Phenomena Of Heat Topic A Thermal Expansion of Solid, Liquid and Gas Answer In Brief:

Question 1. The container has no role in the expansion of which—solid or liquid?
Answer: The container has no role in the expansion of solid.

Question 2. There are two spheres made of the same substance and also have equal radii. One of them is solid and the other is hollow. If the same amount of heat is given to both the spheres, which one expands more?
Answer: The hollow sphere expands more.

Question 3. What is the unit of coefficient of linear expansion of solid?
Answer: The unit of coefficient of linear expansion of solid is °C^-1  or °F^-1 or K^-1.

Question 4. Write one use of a bimetallic strip.
Answer: Bimetallic strip is used as thermostat.

Question 5. A bimetallic strip is made up of two metals A and B. The coefficient of linear expansion of A is more than that of B. If the bimetallic strip is heated, it bends. Which metal remains inside the curvature?
Answer: Metal B remains in the inside portion of the curvature.

Question 6. A bimetallic strip is made up of two metals A and B. The coefficient of linear expansion of A is more than that of B. If the bimetallic strip is cooled, it bends. Which metal remains inside the curvature?
Answer: Metal A remains in the inside portion of the curvature.

Question 7. What is the coefficient of linear expansion of a solid?
Answer: The coefficient of linear expansion of a solid is the fractional increase in length per degree rise in temperature.

Question 8. Does the unit of coefficient of linear expansion of a solid depend on the unit of length?
Answer: No, it does not depend on the unit of length.

Question 9. What is the coefficient of surface expansion of a solid?
Answer: The coefficient of surface expansion of a solid is the fractional increase in area per degree rise in temperature.

Question 10. Does the unit of coefficient of surface expansion of a solid depend on the unit of area?
Answer: No, it does not depend on the unit of area.

Question 11. Define the coefficient of volume expansion of a solid substance.
Answer: The coefficient of volume expansion of a solid is the fractional increase in volume per degree rise in temperature.

Question 12. Does the unit of coefficient of volume expansion of a solid depend on the unit of volume?
Answer: No, it does not depend on the unit of voiume.

Question 13. A scale made of brass is graduated at 0°C. What error may arise in the measurement of a certain distance with this scale at 30°C?
Answer: If a distance is measured by the given scale at 30°C, the reading obtained is less than the actual length.

Question 14. A scale made of brass is graduated at 0°C. 1 What error may arise in the measurement of a certain distance with this scale at 10°C?
Answer: If a length is measured by the given scale at 10°C, the reading obtained is more than the actual length.

Question 15. Why can a platinum wire be easily sealed l with glass by application of heat? 
Answer: As the coefficient of linear expansion of glass and platinum are nearly equal, a platinum wire can be easily sealed with glass by, application of heat.

Question 16. Why cannot a copper wire be sealed with glass by application of heat?
Answer: As the coefficient of linear expansion of copper is greater than that of glass, a copper wire cannot be sealed with glass by application of heat.

Question 17. Name an alloy whose coefficient of thermal expansion is much less than the same of its constituents.
Answer: Invar, an alloy with 36% nickel and 64% iron, has very low coefficient of thermal expansion compared to that of its constituent elements.

Question 18. A liquid is kept in a vessel whose coefficient of volume expansion is 5 x 10^-6 °C^-1. if the real coefficient of expansion of the liquid is 20 x 10^-5 °C^-1, then what is the value of apparent coefficient of expansion?
Answer: Coefficient of apparent expansion of the liquid = coefficient of real expansion of the liquid — coefficient of volume expansion of the substance of the vessel = (20 x 10^-5– 5 x 10^-6) °C^-1 = 19.5 X 10^-5 °C^-1

Question 19. A liquid is kept in two vessels A and B separately and then both are heated. The coefficient of volume expansion of the substance A is greater than that of B. The coefficient of apparent expansion of the liquid is greater in which vessel?
Answer: The coefficient of apparent expansion of the liquid is greater in the vessel B.

Question 20. A spherical metallic ball is heated. Among the radius, surface area and volume, which has the highest percentage increase?
Answer: The volume of the sphere has the highest percentage increase.

Question 21. A spherical metallic ball is heated. Among the radius, surface area and volume, which has the lowest percentage increase?
Answer: The radius of the sphere has the lowest percentage increase.

Question 22. Which coefficient of expansion of a liquid does not depend on the expansion of the container?
Answer: The coefficient of real expansion of a liquid does not depend on the expansion of the container.

Question 23. Which coefficient of expansion of a liquid depends on the expansion of the container?
Answer: The coefficient of apparent expansion of a liquid depends on the expansion of the container.

Question 24. What is the nature of the coefficient of volume expansion of a substance whose volume decreases with increase in temperature?
Answer: The coefficient of volume expansion of a substance, whose volume decreases with increase in temperature, is negative.

Question 25. The coefficient of volume expansion of water is negative in the temperature range of 0°C-4°C. Does the volume of water increase or decrease with an increase in temperature, in the given temperature range?
Answer: The volume of water decreases with an increase in temperature, in the given temperature range.

Question 26. Name one liquid substance whose coefficient of volume expansion is negative in a definite temperature range.
Answer: The value of coefficient of volume expansion of water is negative in the temperature range of 0°C-4°C.

Question 27. Name one solid substance whose coefficient of volume expansion is negative in a definite temperature range.
Answer: The value of coefficient of volume expansion of pure silicon (a solid substance) is negative in the temperature range of -153°C to -255°C.

Question 28. What is the dimensional formula of the coefficients of apparent and real expansion of a liquid?
Answer: The dimensional formula of the coefficients of apparent and real expansion of a liquid is Θ^-1.

Question 29. Define volume coefficient (γ_p) of a gas.
Answer: If the temperature of a gas is raised from 0°C to 1°C by keeping the pressure on a definite mass of gas constant, then the expansion in volume per unit volume of the gas is called the volume coefficient of that gas and it is expressed as γ_p.

Question 30. What is the unit of volume coefficient of gas?
Answer: The unit of volume coefficient of gas is °C^-1  or °F^-1 or K^-1.

Question 31. What is the dimensional formula of volume coefficient of gas?
Answer: The dimensional formula of volume coefficient of gas is Θ^-1.

Question 32. What is the value of volume coefficient of gas?
Answer: The value of volume coefficient of the gas, γ_p= 1/273 °C^-1

Question 33. Is the volume coefficient of gas different for different gases?
Answer: No, the volume coefficient of gas is the same for different gases.

Question 34. The figure 1/273 used in Charles’ law denotes the value of which coefficient of expansion?
Answer: The figure 1/273 used in Charles’ law denotes the value of the coefficient of volume expansion of gas.

Question 35. A beaker at 4°C temperature is filled with a liquid to the brim. The liquid overflows if the temperature is increased. Is the coefficient of volume expansion of the liquid positive or negative?
Answer: The coefficient of volume expansion of the liquid is positive.

Question 36. A beaker at 4°C temperature is filled with a liquid to the brim. The liquid overflows if the temperature is decreased. Is the coefficient of volume expansion of the liquid positive or negative?
Answer: The coefficient of volume expansion of the liquid is negative.

Question 37. Between the coefficients of apparent and real expansion of a liquid, which one has greater value?
Answer: The coefficient of real expansion of a liquid is greater than the coefficient of apparent expansion.

Question 38. Is it possible to construct a liquid thermometer with a glass tube if the coefficients of volume expansion of the liquid and glass are the same?
Answer: No, it is not possible because the level of liquid in the tube remains unchanged with increase in temperature.

Question 39. If value of a in Celcius and Fahrenheit scale are α_c and α_F respectively, then what is the relation between α_c and α_F?
Answer: α_c = 9/5 . α_F

Question 40. Name the substance whose length remains unchanged with the change in temperature.
Answer: Invar.

Question 41. Coefficient of apparent expansion in case of gas is not taken into account’ Why?
Answer: Because volume expansion coefficient of a gas is nearly 100 times more than that of solid.

Question 42. What do you mean by linear expansion coefficient of iron which is or = 12 x 10^-6 /°C ?
Answer: Linear expansion coefficient for iron is a = 12 x 10^-6 /°C means that an iron rod of length 1cm or 1ft or 1 m, when heated through 1°C, will expand by 12 x 10^-6 cm or 12 x 10^-6 ft or 12 x 10^-6 m respectively.

Question 43. If α_c of copper is 17.0 x 10^-6/°C, what is the volume of α_k ?
Answer: As α_c = α_k  Hence aK of copper is =17 x 10^-6 /K.

Question 44. Which one is fundamental property of a liquid-coefficient of apparent expansion or coefficient of real expansion?
Answer: Coefficient of real expansion of liquid is fundamental property of a liquid.

Question 45. What is the coefficient of linear expansion of iron if its coefficient of volume expansion is 36 x 10^-6/°C?
Answer: The coefficient of linear expansion of iron (α) = 1/3 the coefficient of linear expansion of iron (γ) = 1/3 x 36 x10^-6 = 12 x 10^-6/°c

Question 46. Mention a name of an electrical appliance in which thermostat is used.
Answer: Refrigerator.

Question 47. Among solids, liquids and gases which expands less on application of heat?
Answer: Among solids, liquids and gases solids expand less on application of heat.

Chapter 4 Phenomena Of Heat Topic A Thermal Expansion of Solid, Liquid and Gas Fill In The Blanks:

Question 1. The unit of coefficient of linear expansion of any solid substance depends only on the unit of_______
Answer: Temperature

Question 2. If the coefficient of linear expansion of any solid substance in Celcius scale is 18 x 10^-6 /°C, then its value in Fahrenheit scale is ________
Answer: 10 x 10^-6 /°F

Question 3. Thermal expansion of solid is of _______ types.
Answer: Three

Question 4. Increase of length of a solid substance = ________ x coefficient of linear expansion x increase in temperature.
Answer: Initial length

Question 5. If a stopper made of brass is stuck in a bottle made of steel, the bottle has to be _________ in order to open the stopper.
Answer: Heated

Question 6. The coefficient of ________ expansion of a liquid is its inherent property.
Answer: Real

Question 7. If the coefficient of apparent expansion of a liquid is zero, then the level of liquid in a tube remains ________
Answer: Unchanged

Question 8. For accurate measurement during expansion of a gas, volume at ________ is taken as the initial volume.
Answer: 0°C

Question 9. While measuring the coefficient of volume expansion of a gas, pressure remains _________
Answer: Constant

Question 10. Coefficient of real expansion of liquid = coefficient of real expansion of container ________
Answer: Coefficient of apparent expansion

Question 11. ______ is the device which is used for automatic temperature control.
Answer: Thermostat.

Question 12. The coefficient of real expansion is an ________ property of a liquid.
Answer: Intrinsic

Question 13. On heating a bimetallic strip, made by riveting together with a strip of iron and an equal strip of brass, bends so that, the is on _______ the convex side of the curve.
Answer: Brass

Question 14. Density of liquids ________ with increase in temperature.
Answer: Decrease

Chapter 4 Phenomena Of Heat Topic A Thermal Expansion of Solid, Liquid and Gas State Whether True Or False:

Question 1. The coefficient of volume expansion at constant pressure is the same for all ideal gases.
Answer: True

Question 2. The unit of coefficient of apparent expansion of a liquid depends on the unit of temperature.
Answer: True

Question 3. The unit of coefficient of real expansion of a liquid depends on the unit of volume.
Answer: False

Question 4. Thermal expansion of invar is less than that of all other metals or alloys.
Answer: True

Question 5. The thermal expansion of a liquid is generally greater than the thermal expansion of an equal volume of a solid for the same increase in temperature.
Answer: True

Question 6. The thermal expansion of a liquid is generally greater than the thermal expansion of an equal volume of a gas for the same increase in temperature.
Answer: False

Question 7. Coefficient of real expansion of water from 0°C to 4°C is positive.
Answer: False

Question 8. The value of the volume coefficient of a gas is 1/273 °C^-1
Answer: True

Question 9. The value of the pressure coefficient of a gas is 1/273 °C^-1
Answer: True

Question 10. In case .of heat conduction through a bi-metallic strip, the rate of thermal conduction for the two plates remains the same.
Answer: True

Chapter 4 Phenomena Of Heat Topic A Thermal Expansion of Solid, Liquid and Gas Numerical Examples:

1. If the length of a rod at temperature t₁ is l₁ and the length becomes l₂ when the temperature is raised to t_2.

(1)Coefficient of linear expansion, \(\alpha=\frac{l_2-l_1}{l_1\left(t_2-t_1\right)}\)
(2) If the initial temperature t₁ = 0°C and the corresponding length of the rod is l₁ = l_0, then at temperature t°C length of the rod is  l_t = l₀( 1 + αt) .

2. If the value of α in Celsius and Fahrenheit scales are α_c and α_F then, α_c= 9/5 α_F

3. If the surface area of a solid at temperature t₁ is S₁ and that at temperature t₂ is S₂ then, coefficient of surface expansion, \(\beta=\frac{S_2-S_1}{S_1\left(t_2-t_1\right)}\)
(1) S_t = S₀(1 +βt)
(2) β_c = 9/5  β_F

4. If the volume of a solid at temperature t₁ is V₁  and that at temperature t₂ is V₂ then, coefficient of volume expansion, \(\gamma=\frac{V_2-V_1}{V_1\left(t_2-t_1\right)}\)

(1)V_t = V₀(1+γT)
(2)γ_c= 9/5 γ_F
(3)α = β/2 = γ/2

5. The coefficient of real expansion of a liquid (γ_r) = the coefficient of apparent expansion of a liquid (γ_a ) + the coefficient of volume expansion of the material of the container (γ_g ) . ie. γ_r = γ_a + γ_g
6. At constant pressure the volume of a fixed mass of gas at a 0°C and t°C are V₀ and V_t respectively, then V_t  = V₀ (1 + γ_pt) and, \(\gamma_p=\frac{V_t-V_0}{V_0 t}\)
∴γ_p = coefficient of  volume expansion at fixed pressure

Question 1. The lengths of an iron rod are 50 cm and 50.03 cm at 0°C and S0°C respectively. What is the value of coefficient of linear expansion of iron?

Answer: Initial temperature of iron rod (t₁) = 0°C and initial length (l₁) = 50 cm
Final temperature (t₂) = 50°C and final length (l₂) = 50.03 cm
Hence, coefficient of linear expansion of iron,

\(\alpha=\frac{l_2-l_1}{l_1\left(t_2-t_1\right)}\) or, \(\alpha=\frac{50.03-50}{50(50.0)}\) or, \(\alpha=\frac{0.03}{50 \times 50}\) or, α = 12 Χ 10^-6 °C

Question 2. The radius of a circular ring of copper is 5 cm. What is the new radius if the temperature is increased by 200°C ? Coefficient of linear expansion of brass, α =17 x 10⁶/°C

Answer: Initial radius of the ring (r₁ ) = 5 cm
Increase of temperature (t) = 200°C

Thus, final radius of the ring,  r₂= r₁( 1 + αt) or, r₂ = 5(1 + 17 x 10^-6 x 200) = 5.017cm

Question 3. The distance between two railway stations 10 km. The temperature of the place fluctuates between 10°C and 45°C in the whole year. If railway lines are to be laid in between these two stations, how much gap has to be given for safety of the line? Coefficient of linear expansion of steel, α = 12 x 10^-6/°C.

Answer: Length of rail line (L) – 10 km = 10000 m Difference between highest and lowest temperature (t) = (45 – 10)°C = 35°C
Suppose, a gap of Z has to be kept for safety of railway lines.
∴ I = L α t or, l = 10000 x 12 x 10^-6 x 35 or, l= 4.2 m .

Question 4. If the temperature of a metal sphere is increased by 50° C, its volume increases by 03%. What is the value of coefficient of volume expansion of the metal?

Answer: If the initial volume of the sphere is V, then expansion of volume = 0.3V/100 and increase in temperature = 50°C
Hence, value of coefficient of volume expansion of this metal,

\(\gamma=\frac{\frac{0.3 V}{100}}{V \times 50}\) or, γ = 60 x 10^-6/(°C)

Question 5. With reference to glass, the coefficient of volume expansion of mercury is 15.3 X 10^-5/°C. If the coefficient of volume expansion of glass is 27 x 10^-6/°C, what is the value of coefficient of real expansion of mercury?

Answer: Coefficient of apparent expansion of mercury, 15.3 X 10^-5/°C
Coefficient in volume expansion of glass, yg = 27 X 10^-6/°C = 2.7 X 10^-5/°C

∴ coefficient of real expansion of mercury,γ_r = γ_a + γ_g  or, γ_r =15.3 x 10^-5 + 2.7 x 10^-5 = 18 x 10^-5/°C

Question 6. There is 500 cm³ of mercury at 0°C in a glass vessel. If the apparent and real expansion of mercury at 100 °C are 7,65 cm³ and 9 cm³ respectively, calculate the coefficients of apparent and real expansion of mercury.

Answer:

Given

There is 500 cm³ of mercury at 0°C in a glass vessel. If the apparent and real expansion of mercury at 100 °C are 7,65 cm³ and 9 cm³ respectively,

Initial volume of iron = 500 cm³
Increase in temperature = (100-0)°C = 100°C
Apparent expansion of mercury = 7.65 cm³
Real expansion of mercury = 9 cm³

The coefficient of real expansion of mercury,

\(\gamma_a=\frac{\text { apparent expansion }}{\begin{array}{c}
\text { initial volume } \times \\
\text { increase in temperature }
\end{array}}=\frac{7.65}{500 \times 100}\) = 15.3 x 10^-5/°C

The coefficient of real expansion of mercury,

\(\gamma_r=\frac{\text { apparent expansion }}{\begin{array}{c}
\text { initial volume } \times \\
\text { increase in temperature }
\end{array}}=\frac{9}{500 \times 100}\) = 18 x 10^-5/°C

Question 7. The volume of a definite mass of a gas at . 0°C is 100 cm³ and its volume at constant pressure and 20°C is 107.33 cm³. Calculate the coefficient of volume expansion of gas.

Answer:

Given

The volume of a definite mass of a gas at . 0°C is 100 cm³ and its volume at constant pressure and 20°C is 107.33 cm³.

Volume of the gas (V₀ ) at 0°C = 100 cm³
Final temperature (t) = 20°C
Final volume (V_t) = 107.33 cm³

Hence, coefficient of volume expansion of the gas,

\(\gamma_p=\frac{V_t-V_0}{V_0 t}\) or, \(\gamma_p=\frac{107.33-100}{100 \times 20}\) or, γ_p = 3.665 x 10^-3/°C

Question 8. The volumes of a definite mass of a gas at constant pressure and at 50°C and 100°C temperature are 323 cm³ and 373cm³, respectively. Calculate the coefficient of volume expansion of the gas.

Answer:

Given

The volumes of a definite mass of a gas at constant pressure and at 50°C and 100°C temperature are 323 cm³ and 373cm³, respectively.

Suppose, volume of the gas at 0°C = V₀ and coefficient of volume expansion = γ_p
At temperature t₁ = 50°C, volume of the gas, V₁= 323 cm3.
∴ V₁ = V₀ (1 + t_1.γ_p) ……(1)

Again, at temperature t₂ = 100°C, volume of the gas, V₂= 373 cm³
∴ V₂ = V₀ (1 + γ_{p •} t2) …….(2)

If (1) is divided by (2), we get  \(\frac{V_1}{V_2}=\frac{1+\gamma_p \cdot t_1}{1+\gamma_p \cdot t_2}\)

or, \(\frac{323}{373}=\frac{1+50 \gamma_p}{1+100 \gamma_p}\)

or, 323 + 32300 γ_p = 373 + 18650 γ_p
or, 32300 γ_p – 18650yp γ_p = 373 – 323
or, 13650 γ_p = 50

or, \(\gamma_p=\frac{50}{13650}=\frac{1}{273}\)
∴ γ_p =1/273/°C

Question 9. Coefficient of apparent expansion of fmercury with respect to glass is 153 x 10^-6 °C^-1 , where coefficient of real expansion of mercury Is I8O x 10^-6 °C^-1. Find the volume expansion coefficient of glass.

Answer:

Given

Coefficient of apparent expansion of fmercury with respect to glass is 153 x 10^-6 °C^-1 , where coefficient of real expansion of mercury Is I8O x 10^-6 °C^-1.

Coefficient of real expansion of mercury (γ_r) = coefficient of apparent expansion of mercury (γ_a) + coefficient of volume expansion of glass (γ_g)

or, 180 x 10^-6 = 153 x 10^-6 + γ_g
∴ γ_g = 180X 10^-6 – 153 x 10^-6 = 27 x 10^-6
∴ Volume expansion coefficient of glass is 27 x 10^-6 °C^-1  

Wbbse Class 10 Physical Science Chapter 4 Question Answer

Question 10. A liquid has a coefficient of apparent expansion 180 x 10^-6 °C^-1 for an iron container, and 144.6 X 10^-6°C^-1 for an aluminium container. If the coefficient of volume expansion of iron is 36 x 10^-6 °C^-1, find that of aluminium .

Answer:

Given

A liquid has a coefficient of apparent expansion 180 x 10^-6 °C^-1 for an iron container, and 144.6 X 10^-6°C^-1 for an aluminium container. If the coefficient of volume expansion of iron is 36 x 10^-6 °C^-1,

For iron container, γ = γ_a + γ_iron, symbols have usual meanings = 180 x 10^-6 + 36 x 10^-6 = 216 x10^-6

For aluminium container, γ = γ_a +γ_AI  or, 216 x 10^-6 = 144.6 x 10^-6 x γ_A,

∴ γ_AI= 216 X 10^-6– 144.6 X 10^-6 = 71.4 X 10^-6
∴ Volume expansion coefficient of aluminium is 71.4 x 10^-6 °C^-1 .

Question 11. The internal volume of a glass flask is V cm³  . What volume of mercury should be kept in the flask so that the volume of the empty space remains constant at any temperature? Real expansion of mercury r= 180 x 10^-6 °C^-1 and volume expansion of glass =25 x 10^-6 °C^-1 .

Answer: Let, the volume of mercury be x cm³  .

To keep the volume of the empty space constant at any temperature, the expansion of mercury should be equal to that of the glass flask for the same rise in temperature. If the temperature rise is t°C,then x x 180 x 10^-6 x t = V x 25 x 10^-6 x t or Χ = 25V/180 = 5/36 V
∴ 5/36 V cm³  of mercury should be kept in the flask.

Chapter 4 Phenomena Of Heat Topic B Thermal Conductivity Synopsis:

1. Flow of heat from one place to another is called transmission of heat.
2. Heat is transmitted in three different process—conduction, convection and radiation. .
3. The process in which heat flows from a higher temperature region to a lower temperature region of a material without any displacement of material particles is called conduction.

4. Materials which can conduct heat easily are called thermal conductors.
5. Materials which cannot conduct heat easily are called bad conductor of heat or thermal insulators. Fibre glass, paper, cork, water, wood, glass etc are bad conductors of heat.

6. During transmission of heat through any object if both conduction and absorption go on simultaneously, it is called pre-steady state condition of heating.
7. In pre steady state heat conduction through a rod depends on both 0 the coefficient of thermal conductivity and specific heat of the material of the rod.
8. In steady state only conduction of heat takes place not absorption.

9. In steady state heat conduction along a rod depends only on the coefficient of thermal conductivity of its material. The coefficient of thermal conductivity of material is defined as the quantity of heat that conducts per unit time through unit area of the material keeping its opposite faces at a temperature difference of one degree, when the steady state has been reached.

Let a rectangular plate of cross sectional area A and thickness d maintain temperatures θ₁ and θ₂ on its two opposite faces where θ₁>θ₂ . in this condition heat passes perpendicularly through the slab from the hotter surface to the colder surface. If θ amount of heat is transferred perpendicularly across the plate in time t in steady state then it is observed experimentally that,

(1)Q is directly proportional to A i.e., Q ∝ A
(2)Q is directly proportional to (θ₁ – θ₂) i.e., Q ∝ (θ₁ – θ₂)
(3)Q is directly proportional to t, i.e., Q ∝ t
(4)Q is inversely proportional to d i.e., Q α 1/d

Hence,\(Q \propto \frac{A\left(\theta_1-\theta_2\right) t}{d}\)

or, \(Q=k \cdot \frac{A\left(\theta_1-\theta_2\right) t}{d}\) k is a constant

The value of the constant depends on the material of the plate. k is known as the coefficient of thermal conductivity.

10. For ideal conductor k is infinity and for an ideal insulator k= 0.

Wbbse Class 10 Physical Science Chapter 4 Question Answer

Units of k: In CGS system, \(calorie $\cdot \mathrm{cm}$
$\mathrm{cm}^2 \cdot{ }^{\circ} \mathrm{C} \cdot$ second\) = cal. cm^-1. °C^-1.s^{-1 .}

In SI it is J. m^-1 . K^-1 . s^-1= W . m^-1 . K^-1

We know that, \(k=\frac{Q \cdot d}{A\left(\theta_1-\theta_2\right) t}\)

∴ Dimensional formula of k, \(=[k]=\frac{\mathrm{ML}^2 \mathrm{~T}^{-2} \times \mathrm{L}}{\mathrm{L}^2 \cdot \Theta \times \mathrm{T}}\) = \(=\mathrm{MLT}^{-3} \Theta^{-1}\)

12. Silver have highest thermal conductivity among metals [k = 406 SI unit)
13. Diamond is the best thermal conductor {k^ 1000 SI unit)
14. Among liquids, mercury is the best conductor {k = 8.3 SI unit)
15. Thermal conductivity of vacuum is zero.

16. Thermal resistance is defined as the property of a substance by which it resists the flow of heat through it.

Electrical resistance (R) = \(=\frac{\text { potential difference }\left(V_1-V_2\right)}{\text { intensity of electric current }(I)}\)

Thermal resistance = \(=\frac{\text { temperature difference }\left(\theta_1-\theta_2\right)}{\text { heat current }(H)}\) = \(=\frac{\left(\theta_1-\theta_2\right)}{Q / t}\)

[Heat current (H) = flow of heat (Q)/ time (t)]

From the relation of k we get, \(Q=\frac{k \cdot A\left(\theta_1-\theta_2\right) t}{d}\) ,\(\text { or, } \frac{\left(\theta_1-\theta_2\right)}{Q / t}=\frac{d}{k \cdot A}\)

Electrical resistance,\(R=\rho \cdot \frac{l}{A}\) [p = resistivity, l = length, A = area of cross section]

So, 1/k is similar to p
Hence 1/k is called thermal Resistivity.

17. Similarities between heat conduction and electrical conduction:

18. Dissimilarities between heat conduction and electrical conduction:

Chapter 4 Phenomena Of Heat Topic B Thermal Conductivity Short And Long Answer Type Questions:

Question 1. What is conduction? Write down the characteristics of transmission of heat in the process of conduction.

Answer:

Conduction

It is the method in which heat is transmitted from a warmer place of the substance to a colder place without any displacement of the molecules.

In the conduction process:
1. A solid medium is required for heat transmission.
2. The medium becomes hot during heat transmission.
3. There is no displacement of the molecules of the medium at the time of heat transmission.
4. Heat can be transmitted along any of straight or curved path.

Question 2. What do you mean by pre-steady state condition in case of conduction of heat? Demonstrate with the help of an experiment that the capacity of heat conduction is different for different substances.

Answer:

Pre-steady state condition in case of conduction of heat

During transmission of heat through any object if both conduction and absorption go on simultaneously, it is called pre-steady state condition of heating.

Experiment: A rectangular, metallic vessel is taken. Three holes are made on its wall in the same height. Three different metal rods (say of copper, aluminium and iron) of same length and same cross sectional area are inserted through the holes. The portion of the rods outside the vessel are wax-coated.

Next, water is poured in the vessel and then it is heated uniformly by a bunsen burner. In this condition heat conducts along the lengths of the rods. After some time, it is seen that wax has melted in all the rods but up to different lengths.

Conclusion: It is clearly understood from this experiment that the capacity of conducting heat is different for different substances. If wax melts up to l₁, l₂ and l₃ on copper, aluminium and iron rods respectively, it is observed that l₁ > l₂ > l₃

Question 3. What is thermal conductivity? Suppose the thickness of a rectangular plate is d, its cross-sectional area is A and the temperature of its opposite sides are θ₁ and θ₂ respectively (where θ₁ > θ₂). At thermal steady state, if Q amount of heat is transmitted perpendicularly in time t from the hotter side to the colder side then how can you express thermal conductivity of the substance of the plate?

Answer:

Thermal conductivity

The thermal conductivity of a substance is defined as the heat conducted perpendicularly in one second across the opposite faces of a cuboid of unit cross-sectional area and unit thickness when the difference in temperature of its two opposite faces is unity.

By experiment, it has been seen that:
1. Q ∝ A
2. Q∝(θ₁-θ₂)
3. Q ∝1/d
4. Q ∝ t

According to the rule of compound variation, \(Q \propto \frac{A\left(\theta_1-\theta_2\right) t}{d}\) or, \(Q=\frac{k A\left(\theta_1-\theta_2\right) t}{d}\)

∴ \(k=\frac{Q \cdot d}{A\left(\theta_1-\theta_2\right) t}\)

where k is a constant, known as the thermal conductivity of the substance of the plate.

Question 4. Find out the unit of thermal conductivity. Establish a relationship between the units thermal conductivity in CGS system and SI.

Answer: From definition, we have thermal conductivity, K = Q . d/Aθt
Where d= thickness, A= cross-section area, = temperature difference, t= time and Q = heat.

So,unit of k(in SI) = \(=\frac{J \times m}{m^2 \times K \times s}\) = J . m^{-1 .}  K^{-1 .} s^-1    and in CGS it is cal.cm^{-1 .}  K^{-1 .} s^-1

1 cal.cm^-1.  C^{-1 .} s^-1= 42J. (10^-2m)^-1 K^{-1 .} s^-1  = 420W.m^-1.  K^{-1 .} 

Question 5.  What do you mean by thermal resistance? What is the unit of thermal resistance?

Answer:

Thermal resistance

Thermal resistance is defined as the property of a substance by which it resists the flow of heat through it.

Let the thickness of a body be d, its cross-sectional area be A and the thermal conductivity of its substance be k.

Therefore, its thermal resistance is d/kA.
Thermal resistance, = \(\frac{d}{k A}=\frac{\theta_2-\theta_1}{Q / t}=\frac{\left(\theta_2-\theta_1\right) t}{Q}\)

Now, unit of (θ₂-θ₁) is kelvin (K), unit of t is second (s), unit of Q is the joule (J). Hence, unit of thermal resistance is K. s. J-¹.

Question 6. How is the thermal resistance of a conductor compared with its electrical resistance?

Answer: The cause of an electric current(l) through a conductor is the potential difference(V) between its two ends.

According to Ohm’s law V= IR or, \(R=\frac{V}{l}=\frac{V}{\left(\frac{q}{t}\right)}\)…….(1)

Similarly, the cause of conduction of heat through a conductor is the difference of temperature at the two ends of the conductor(θ).

Thus, amount of heat conducted, \(Q=k \cdot A \frac{\theta}{d} \cdot t\) or \(\frac{d}{k A}=\frac{\theta}{\left(\frac{Q}{t}\right)}\) …..(2)

There is somewhat similarity between equation (1) and equation(2). In this way, the quantity(d/kA) is similar to R. Thius is the thermal resistance of a conductor.

Question 7. I = q/t = V/R and \(\frac{Q}{t}=k \cdot A \cdot \frac{\left(\theta_2-\theta_1\right)}{d}\)
What are the similarities between different quantities in these two equations? [The symbols represent conventional physical quantities]

Answer:

The similarities in the two equations are shown:

Type	Electrical quantities	Quantity related to heat conduction
Quantity	Electrical charge (q)	Heat (Q)
Property	Potential difference (V)	Difference of temperature (θ2 – θ1  )
Rate of flow	Current ( I = q/t)	Rate of conduction of heat (Q/t)
Resistance	Electrical resistance (R)	Thermal resistance (d/kA)

Question 8. Define conductor and insulator of heat. Why is the handle of a kettle wrapped with cane?

Answer:

Conductor and insulator of heat.

1. Conductors of heat are those substances through which heat can be conducted easily. For example, iron.
2. Insulators of heat are those substances through which heat cannot be conducted easily. For example, wood.

3. Kettle is generally made of aluminium. Aluminium is a good conductor of heat. When water or any other liquid is heated in a kettle, the kettle also becomes hot along with the liquid inside it. In this condition, it is Very difficult to touch the handle of the kettle. Cane is an insulator of heat. So, if cane is wrapped on the handle of the kettle, no heat is transmitted to the hand and the handle can be touched easily. For this reason, the handle of a kettle is wrapped with a cane.

Question 9. If we touch two chairs, one of wood and the other of iron, both at the same temperature during winter, why does the iron chair feel colder than the other? In which condition they feel same in temperature?

Answer:
1. Our body temperature generally remains higher than the temperature of a chair during winter. Wood is a bad conductor of heat but iron is a good conductor of heat. If we touch an iron chair, heat is transmitted very quickly from our body to the chair but when we touch a wooden chair, conduction of heat is very slow.

2. This is why the iron chair feels colder. As the temperature of the chair becomes equal with one’s body temperature, they feel same in temperature.

Wbbse Class 10 Physical Science Chapter 4 Question Answer

Question 10. Let us take a rod, half of which is made of wood and the other half is made of copper; The rod is wrapped with a thin paper. Now it is held directly over the flame of a burner. Explain what happens.

Answer: If the rod is held directly over the flame of a burner, it is seen that the paper surrounding the wooden portion is burnt immediately but the paper surrounding the copper side is not burnt. Copper being a good conductor .of heat, heat is conducted evenly all over the rod and the temperature of the paper does not reach the ignition point.

But in the case of wood which is a bad conductor of heat, heat is not conducted. As a result, the temperature reaches the ignition point and the paper is burnt. But if held for a long time, the paper on the copper part also gets burnt.

Question 11. Why the birds fluff up their feathers during winter?

Answer: During winter the birds fluff up their feathers to keep themselves warm. When the birds fluff up their feathers, feathers trap air in them. As air being an insulator, does not allow heat from the body to escape. So the birds keep warm.

Question 12. Wearing of two relatively fiver clothes instead of a thick cloth is more comfortable. Why?

Answer:

Wearing of two relatively fiver clothes instead of a thick cloth is more comfortable.

If we wear two relatively fiver clothes instead of a thick cloth, we feel warmer. This happens because the two clothes trap a layer of air between them. Air is a thermal insulator and so it prevents the heat from our body from escaping. So we feel warm and more comfortable.

Chapter 4 Phenomena Of Heat Topic B Thermal Conductivity Very Short Answer Type Questions Choose The Correct Answer:

Question 1. Which of the following metals has the highest conductivity?
1. Copper
2. Aluminium
3. Silver
4. Gold

Answer: 3. Silver

Question 2. The value of thermal conductivity of an ideal conductor (in the unit of cal • cm^{-1. °}C^{-1 .} s^-1) is
1. 0
2. 1
3. 100
4. ∞

Answer: 4. ∞

Question 3. The value of thermal conductivity of an ideal insulator (in the unit of cal • cm^-1 • °C^-1  • s^-1) is
1. 0
2. 1
3. 100
4. ∞

Answer: 1. 0

Question 4. At steady state,
1. Both conduction and absorption of heat take place
2. Neither conduction nor absorption of heat takes place
3. Only absorption of heat takes place, not conduction
4. Only conduction of heat takes place, not absorption

Answer: 4. Only conduction of heat takes place, not absorption

Question 5. The value of the thermal conductivity of a substance is 42 W • m^-1  K^-1. What is its value in CGS unit?
1. 0.1
2. 0.12
3. 0.13
4. 0.15

Answer: 1. 0.1

Question 6. Dimensional formula of thermal resistance is
1. M^-1L^-2T^-3 Θ^-1
2. M^-1L^-3T³ Θ
3. ML^-2T³ Θ
4. M^-1L^-2T³ Θ

Answer: 4. M^-1L^-2T³ Θ

Question 7. What is the power of L in the dimensional formula of thermal conductivity?
1. 1
2. 2
3. -1
4. -2

Answer: 1. 1

Question 8. Diamond is
1. Good conductor of heat and electricity
2. Bad conductor of heat and electricity
3. Bad conductor of heat, good conductor of electricity
4. Good conductor of heat, bad conductor of electricity

Answer: 4. Good conductor of heat, bad conductor of electricity

Question 9. Which of the following is a good conductor of heat?
1. Cork
2. Air
3. Wood
4. Graphite

Answer: 4. Graphite

Question 10. A rectangular plate has thickness = d, cross sectional area = A and thermal conductivity = k. What is the value of thermal resistance?
1. d/kA
2. kA/d
3. dA/k
4. A/kd

Answer: 1. d/kA

Question 11. What is the increase in area of a substance if the coefficient of its surface expansion = 2 x 10^-5°C^-1, initial area = 104 cm² and increase of temperature = 100°C?
1. 21 cm² 
2. 20 cm² 
3. 22 cm²
4. 23 cm² 

Answer: 2. 20 cm² 

Question 12. In which case the thermal conductivity increases from left to right?
1. Al, Cu, Ag
2. Ag, Cu, Al
3. Cu, Ag, Al
4. Al, Ag, Cu

Answer: 1. Al, Cu, Ag

Question 13. For cooking food, which of the following type of utensil is most suitable?
1. High specific heat and high conductivity
2. Low conductivity
3. Low specific heat and low conductivity
4. Low specific heat and high conductivity

Answer: 4. Low specific heat and high conductivity

Question 14. Under steady state, the temperature of a body
1. Increases with time
2. Decreases with time
3. Does not change with time and is same at all the points of the body
4. Does not change with time but different at different points of the body

Answer: 4. Does not change with time but different at different points of the body

Question 15. Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in 20 minute and 30 minutes respectively. The ratio of their thermal conductivity will be
1. 3:2
2. 1:1
3. 2:3
4. 4:1

Answer: 1. 3:2

Question 16. The coefficient of thermal conductivity depends upon
1. Temperature difference of two surfaces
2. Area of the plate
3. Thickness of the plate
4. Material of the plate

Answer: 4. Material of the plate

Wbbse Class 10 Physical Science Chapter 4 Question Answer

Question 17. A piece of metal appears colder in winter morning than a piece of wood when touched because
1. Metal has high specific heat
2. Metal has high thermal conductivity
3. Metal has low specific heat
4. Metal has low thermal conductivity

Answer: 2. Metal has high thermal conductivity

Question 18. On heating one end of a rod, the temperature of whole rod will be uniform when,
1. k=1
2. k = 0
3. k = very small
4. k = infinity

Answer: 4. k = infinity

Question 19. Mud houses are cooler in summer and Warmer in winter because
1. Mud is a good conductor of heat
2. Mud is a bad conductor of heat
3. Thermal conductivity of mud is infinite
4. Thermal conductivity of mud is 0

Answer: 2. Mud is a bad conductor of heat

Question 20. If thermal conductivity of a material is k, then it’s thermal resistivity is
1. k
2. 1/k
3.k²
4. 1/k²

Answer: 2. 1/k

Chapter 4 Phenomena Of Heat Topic B Thermal Conductivity Answer In Brief:

Question 1. Name one liquid which is a good conductor of heat.
Answer: Mercury is a liquid which is a good conductor of heat.

Question 2. Name one substance whose electrical conductivity is very low but whose thermal conductivity is very high.
Answer: Diamond has very low electrical conductivity but very high thermal conductivity.

Question 3. What is the value of the thermal conductivity of a diamond?
Answer: The value of thermal conductivity of a diamond is 5.2380 cal • cm^-1. s^-1. K^-1    or, 22 W . cm^-1. K^-1 (approx.).

Question 4. Name the substance with the highest thermal conductivity at room temperature.
Answer: According to the latest available information, monocrystalline synthetic diamond has the highest thermal conductivity at room temperature.

Question 5. What is the thermal conductivity of monocrystalline synthetic diamond at room temperature?
Answer: The thermal conductivity of monocrystalline synthetic diamond at room temperature is 33.2 W • cm^-1. K^-1 (approx.).

Question 6. State whether diamond or copper has the higher value of thermal conductivity.
The thermal conductivity of diamond is approximately five times more than that of copper.

Question 7. What is the dimensional formula for thermal conductivity?
Answer: Dimensional formula for thermal conductivity is MLT^-3Θ^-1.

Question 8. What is the unit of thermal conductivity in CGS system?
Answer: Unit of thermal conductivity in CGS system is cal.cm^-1. °C^-1.s^-1 .

Question 9. What is the unit of thermal conductivity in SI?
Answer: Unit of thermal conductivity in SI is W • m^-1 • K^-1.

Question 10. When is the value of the thermal resistance of a substance equal to the reciprocal of its thermal conductivity?
Answer: The value of the thermal resistance of a substance is equal to the reciprocal of its thermal conductivity when its thickness is equal to its cross sectional area.

Question 11. By keeping the length (thickness) of a slab unchanged, if its area of cross section is halved, how many times does its thermal resistance increase?
Answer: By keeping the length (thickness) of a slab unchanged, if its area of cross section is halved, its thermal resistance increases two times.

Question 12. By keeping the area of cross section of a slab unchanged, if the length (thickness) is halved, how many times does its thermal resistance increase?
Answer: By keeping the area of cross section of a slab unchanged, if its length (thickness) is halved, its thermal resistance is also halved.

Question 13. If the thermal conductivity of a substance is k = 0.8 cal • cm^-1. °C^-1. s^-1, what is the value of k in SI?
Answer: The value of thermal conductivity k in SI is 0.8 X 420 W • m^-1 • K^-1 = 336 W • m^-1 • K^-1.

Question 14. When do we feel an iron chair and a wooden chair to be hot to the same extent, by touching?
Answer: We feel the two chairs to be hot to the same extent, when the body temperature and the temperatures of the two chairs become equal.

Wbbse Class 10 Physical Science Chapter 4 Question Answer

Question 15. What are thermal conductors of heat?
Answer:

Thermal conductors of heat

Materials which can conduct heat easily are called thermal conductors of heat.

Question 16. What are insulators or bad conductors of heat?
Answer: Materials which can not conduct heat easily are called insulators or bad conductors of heat.

Question 17. Thickness and area of cross section of a rectangular metallic plate are d and A respectively. Thermal conductivity of the material of the plate is k. What is its thermal resistance?
Answer: Thermal resistance of the plate is d/kA.

Question 18. If thickness and area of cross section of a metallic plate are unchanged then what will be the relation between thermal resistance and thermal conductivity?
Answer: If thickness and area of cross section of a rectangular slab are unchanged then thermal resistance (R) is inversely proportional to the thermal conductivity.

Question 19. If thermal conductivity is k then which physical quantity is denoted by 1/k?
Answer: 1/k denotes the thermal resistivity.

Question 20. Keeping area of cross section of a rectangular slab unchanged, if thickness of the slab is 1/2 of its initial value, then what 2 will be the change in its thermal resistance?
Answer: Thermal resistance will be 1/2 of its initial value.

Question 21. What is the value of thermal conductivity of vacuum?
Answer: The thermal conductivity of vacuum is zero.

Question 22. What is the value of thermal conductivity of an ideal insulator of heat?
Answer: The value of thermal conductivity of an ideal insulator of heat is zero.

Question 23. What is the value of thermal conductivity of an ideal conductor of heat?
Answer: The value of thermal conductivity of an ideal conductor is infinite.

Question 24. In which state of conduction of heat through solids no heat is absorbed by any layer of the solid?
Answer: In steady state there is no absorption of heat by any layer of a solid.

Question 25. In which state of conduction of heat through solids heat is absorbed by different layers of a solid?
Answer: In pre-steady state of conduction of heat through solids some amount of heat is absorbed by the different layers of the solid.

Chapter 4 Phenomena Of Heat Topic B Thermal Conductivity Fill In The Blanks:

Question 1. There is _______displacement of the molecules of the medium during transmission of heat by the conduction process.
Answer: No

Question 2. Thermal conductance of wooden dust is_____ than that of wood.
Answer: Less

Question 3. Thermal conductivity of vacuum is _______
Answer: Zero

Question 4. The value of thermal conductivity of diamond is _______ than that of gold.
Answer: More

Wb Class 10 Physical Science Solutions

Question 5. If the value of thermal conductivity is more, thermal resistance is _______
Answer: Less

Question 6. From _______ experiment it was proved that thermal conductivity of different materials are different.
Answer: Ingenhousz

Question 7. SI unit of thermal resistance is _______
Answer: K/watt

Question 8. Flow of heat from one place to another is called _______ of heat.
Answer: Transmission

Question 9. Conduction usually takes place in ______
Answer: Solids

Question 10. All gases are _____ conductors of heat.
Answer: Bad

Question 11. vacuum can not conduct heat and therefore it is an _______ insulator.
Answer: Ideal

Question 12. Rate of flow of heat is called ______ current.
Answer: Heat

Question 13. The reciprocal of coefficient of thermal conductivity is ______ of the conductor.
Answer: Thermal Resistivity

Question 14. Material medium is necessary for transmission of heat in the process of _____
Answer: Conduction

Question 15. In the process of ______ of heat, heat can travel along a straight or a curved path.
Answer: Conduction

Chapter 4 Phenomena Of Heat Topic B Thermal Conductivity State Whether True Or False:

Question 1. The coefficient of thermal conductivity of a conductor does not depend on the substance of the conductor.
Answer: False

Question 2. All metals are bad conductors of heat.
Answer: False

Question 3. The rate of thermal conduction remains the same if the temperature difference between the two ends of a conducting rod is made twice the previous value.
Answer: False

Question 4. Material medium is necessary for conduction of heat.
Answer: True

Question 5. During conduction of heat through solids, molecules of the solid can move freely.
Answer: False

Question 6. Vacuum is an ideal conductor of heat.
Answer: False

Question 7. Thermal conductivity of diamond is less than that of silver.
Answer: False

Question 8. Silver is the best metallic conductor of heat.
Answer: True

Question 9. Thermal conductivity is the property of a material that, indicates its ability to conduct heat.
Answer: True

Chapter 4 Phenomena Of Heat Topic B Thermal Conductivity Numerical Examples:

1. If the temperatures of the two faces of a rectangular plate of cross sectional area A and of thickness d be θ₁ and θ₂ (θ₁ > θ₂) then the amount of heat conducted in time t from the hot to the cold face of the plate will be,

\(Q=\frac{k A\left(\theta_1-\theta_2\right) t}{d}\)

2. Heat current = \(\frac{Q}{t}=\frac{k A\left(\theta_1-\theta_2\right)}{d}\)

3. Temperature gradient = \(\frac{\theta_1-\theta_2}{d}\)

4. Thermal resistance of a conductor = \(\frac{1}{k} \cdot \frac{d}{A}\)

5. Thermal resistivity of a conductor = 1/k

Wb Class 10 Physical Science Solutions

Question 1. Thickness, surface area and thermal conductivity of two rods are in the ratio 1: 2 . What is the ratio of thermal resistance of the two rods?

Answer:

Given:

Thickness, surface area and thermal conductivity of two rods are in the ratio 1: 2 .

Suppose, thickness, cross sectional area and thermal conductivity of two rods are d₁, d₂: A₁, A₂ and k₁, k₂ respectively.

∴ \(\frac{d_1}{d_2}=\frac{A_1}{A_2}=\frac{k_1}{k_2}=\frac{1}{2}\)

Thermal resistance of the first rod, \(R_1=\frac{d_1}{k_1 A_1}\) and thermal resistance of the second rod, \(R_2=\frac{d_2}{k_2 A_2}\)

∴ \(\frac{R_1}{R_2}=\frac{d_1}{k_1 A_1} \times \frac{k_2 A_2}{d_2}\) or, \(\frac{R_1}{R_2}=\frac{d_1}{d_2} \times \frac{k_2}{k_1} \times \frac{A_2}{A_1}\) or, \(\frac{R_1}{R_2}=\frac{1}{2} \times 2 \times 2\) or, \(\frac{R_1}{R_2}=2\)

Therefore, the ratio of thermal resistance of the two rods is R₁: R₂ = 2:1

Question 2. A and B are two rods of the same length. For each of them, temperature on two sides are T₁°C and T₂°C(T₁> T₂) respectively. Which condition has to be fulfilled in order to have the same rate of transmission of heat through both the rods?

Answer:

Given:

A and B are two rods of the same length. For each of them, temperature on two sides are T₁°C and T₂°C(T₁> T₂) respectively.

Suppose, length of each rod = l, thermal conductivities are k₁ and k₂ respectively and cross sectional areas are A₁  and A₂ respectively. Rate of transmission of heat through both rods are equal.

∴ \(\frac{k_1 A_1\left(T_1-T_2\right)}{1}=\frac{K_2 A_2\left(T_1-T_2\right)}{l}\) or, k₁A₁  = k₂A₂

Therefore, the condition k₁A₁  = k₂A₂ has to be fulfilled in order to have the same rate of transmission of heat through them.

Question 3. The rate of transmission of heat through a rod is 6000 J/s. Its length and cross sectional area are 1m and 0.5 m² respectively. If the thermal conductivity of the rod is k = 200W•m^-1K^-1, what is the difference of temperature between the two sides?

Answer:

Given:

The rate of transmission of heat through a rod is 6000 J/s. Its length and cross sectional area are 1m and 0.5 m² respectively. If the thermal conductivity of the rod is k = 200W•m^-1K^-1,

Length of the rod (d) = lm
Cross sectional area (A) = 0.5 m²
Rate of transmission of heat through the rod(Q/t) =6000 J/s
Suppose, temperature difference between the two sides of the rod = θ°C

∴ \(\frac{Q}{t}=\frac{k A \theta}{d}\) or, \(6000=\frac{200 \times 0.5 \times \theta}{1}\) or, 100θ=6000 or, θ = 60°C

Wb Class 10 Physical Science Solutions

Question 4. Window has an area of 3 m² and thickness of glass of 2 mm . Temperature at the inside and outside of the glass surface are 20°C and -5°C, respectively. What amount of heat is transmitted through the windows to the outside per minubte due to conduction? Thermal conductivity of glass is 0.002 CGS unit.

Answer:

Given:

Window has an area of 3 m² and thickness of glass of 2 mm . Temperature at the inside and outside of the glass surface are 20°C and -5°C, respectively.

Here, k = 0.002 CGS unit A = 3 m²= 3 x 104cm², θ = 2O°C, θ = -5°C, t = 60 s, d = 2 mm = 0.2 cm

We know, \(\mathrm{Q}=\frac{k A\left(\theta_2-\theta_1\right) t}{d}\) = \(\frac{0.002 \times 3 \times 10^4\{20-(-5)\} \times 60}{0.2}\) = 45 104cal

Therefore, an amount of heat of 45x 10⁴ cal is transmitted from the room through each window.
Hence, 2 x 45 x10⁴ caI= 90 x10⁴ cal of heat is transmitted through the two windows.

Question 5. The area of cross section of a metallic rod of length 20 cm is 2 cm². If coefficient of thermal conductivity of the material of the rod is k=0.5 cal. cm^-1 • °C^-1 • s^-1   then find its thermal resistance.

Answer:

Given:

The area of cross section of a metallic rod of length 20 cm is 2 cm². If coefficient of thermal conductivity of the material of the rod is k=0.5 cal. cm^-1 • °C^-1 • s^-1  

Length of the rod (d) = 20 cm, area of cross section of the metallic rod (a) = 2 cm²

∴ Thermal resistance of the rod \(R_T=\frac{d}{k A}=\frac{20}{0.5 \times 2}\) = 20°C^-1 • s • cal^-1

Question 6. Two opposite surfaces of a cuboid of volume 1000 cm³ are kept in contact with steam at 100°C and ice at 0°C respectively. The coefficient of thermal conductivity of the material of the cuboid k = 0.5 cal. cm^-1 • °C^-1 • s^-1 and latent heat of melting of ice = 80 cal/g. What mass of ice will melt in time 8 min?

Answer:

Given:

Two opposite surfaces of a cuboid of volume 1000 cm³ are kept in contact with steam at 100°C and ice at 0°C respectively. The coefficient of thermal conductivity of the material of the cuboid k = 0.5 cal. cm^-1 • °C^-1 • s^-1 and latent heat of melting of ice = 80 cal/g.

Length of a each side of the cuboid (l) = \(\sqrt[3]{100}\) = 10cm

∴ Area of each surface of the cuboid (A) = (10)² = 100 cm²
Temperature difference between two opposite surfaces (θ₁– θ₂ ) = (100 – 0)°C = 100°C
Coefficient of thermal conductivity of the material (k) = 0.5 cal. cm^-1 • °C^-1 • s^-1

Time for conduction of heat (t) = 8 min = 8 x 60 = 480 s
Latent heat of melting of ice (Z.) = 80 cal/g

If, m g ice melts, then, according to the problem, \(m \cdot L=\frac{k \cdot A\left(\theta_1-\theta_2\right) t}{d}\)

or,\(m \cdot 80=\frac{0.5 \times 100(100-0) \cdot 480}{10}\)

or, \(m=\frac{0.5 \times 100 \times 100 \times 480}{80 \times 10}=3000\)

∴ 3000g or 3kg ice will melt.

Question 7. room has a glass window of area 1 m² and thickness 0.5 cm. The inside and the outside temperature of the room are 10°C and 40°C respectively. Find the amount of heat conducted in 10 min through the window if k of the glass is = 0.0012 cal. cm^-1 • °C^-1 • s^-1

Answer:

Given:

Room has a glass window of area 1 m² and thickness 0.5 cm. The inside and the outside temperature of the room are 10°C and 40°C respectively.

Thickness of the glass (d) = 0.5 cm , area of the glass window (A) = 1m² = 10⁴ cm², temperature difference (θ₁ -θ₂) = (40 – 10) = 30°C, time (f) = 10 min = 10 x 60 s = 600 s .

∴ The amount of heat transmitted through the glass window, \(Q=\frac{k A\left(\theta_2-\theta_1\right) \cdot t}{d}\) = \(m=\frac{0.5 \times 100 \times 100 \times 480}{80 \times 10}=3000\) = 4.32 x 10⁵cal

Chapter 4 Phenomena Of Heat Miscellaneous Type Questions Match The Columns:

Question 1.

Column A	Column B
Unit of coefficient of apparent expansion of a liquid	1. M-1L-2T3
Unit of thermal conductivity	2. K-1
Dimensional formula of thermal resistance	3. MLT-3Θ-1
Dimensional formula of thermal conductivity	4. W m-1 K-1

Answer:
Unit of coefficient of apparent expansion of a liquid: 2. K^-1
Unit of thermal conductivity: 4. W m^-1 K^-1 
Dimensional formula of thermal resistance: 1. M^-1L^-2T³
Dimensional formula of thermal conductivity: 3. MLT^-3Θ^-1

Question 2.

Column A	Column B
The metal which has the highest thermal conductivity	1. Water
A liquid which is a good conductor of heat	2. Wood
A substance which has a high thermal resistivity	3. Mercury
A liquid which displays the anomalous expansion	4. Silver

Answer:
The metal which has the highest thermal conductivity: 4. Silver
A liquid which is a good conductor of heat: 3. Mercury
A substance which has a high thermal resistivity: 2. Wood
A liquid which displays the anomalous expansion: 1. Water

WBBSE Solutions for Class 10 Physical Science and Environment