WBCHSE Notes For Class 11 Physics Thermometry

Properties Of Bulk Matter Thermometry

Thermometry deals with the measurement of temperature.
Generally, on touching an object we have some sort of sensation. This sensation is known as thermal sensation which indicates the thermal condition of the object.

1. This thermal sensation enables us to understand
2. Whether a body is hot or cold, and
3. How hot or how cold of a body is compared to other bodies. For example, thermal sensation gives the feeling that the water of a pond is hotter than ice, but is colder than water that has been heated for some time.

Again, if a cold body is in contact with a hot body, the cold one gets gradually hotter and the hot one gets gradually colder. After some time both of the bodies produce the same thermal sensation.

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But thermal sensation often is not completely dependable because,

1. It is unsafe to touch very hot or very cold bodies.
2. The thermal sensation is different for objects that are in contact with one another or in the same environment for a long time. For instance, during the winter a piece of iron feels colder than a piece of wood.
3. Thermal sensation is subjective and may differ from person to person.

• Thus, it is essential to establish a measurement system that can determine the thermal condition of a body accurately and that is independent of a person, place, or environment.
• To achieve this, a law, based on experiences and experimental results, was formulated. This law is the zeroth law of thermodynamics.
• Before discussing the zeroth law of thermodynamics, we should gain a basic notion of two widely used terms in thermal science—thermal contact and thermal equilibrium.

Thermal contact: Thermal contact may exist between two objects even when they do not touch each other. For example, a cup of hot tea kept on a table for quite some time ceases to remain hot.

This happens because the cup of tea and the other objects in the room have thermal contact among them and after a while they produce the same thermal sensation. In the study of thermal science, thermal contact is abbreviated as contact.

Thermal equilibrium: In general, on touching different objects and feeling the same thermal sensation, we say that these objects are in thermal equilibrium. For example, the objects kept in the same room are in thermal equilibrium most of the time.

• Let us consider various objects that are not in thermal equilibrium. If these objects are kept in thermal contact of one another, they attain thermal equilibrium on their own.
• For example, a cup of hot tea kept on a table for quite some time is seen to attain thermal equilibrium with other objects in the room.

Properties Of Bulk Matter – The Zeroth Law Of Thermodynamics

Thermodynamics is the branch of physics that discusses the mutual conversion between heat and work and the changes in the physical properties of different bodies caused by this type of conversion.

• Thermodynamics is based on two fundamental laws—the first and the second laws of thermodynamics. After the two laws were formulated and put in use, the need for the identification of a fundamental property of matter was felt. This property is the temperature of a body.
• Hence, a law was to be formulated that would define temperature. It was reasonable that this law should precede the already existing first and second laws of thermodynamics. Thus this law was named the zeroth law of thermodynamics.

Statement of Zeroth law: If two bodies are sepa¬rately in thermal equilibrium with a third body, then the first two bodies are also in thermal equilibrium with each other.

• For example, if A and B are separately in thermal equilibrium with C, then according to the zeroth law, A and B are also in thermal equilibrium with each other.
• This may appear to be an obvious truth and we are tempted to believe that the statement need not be considered as a separate law. But it is not true our experiences dictate that this type of argument does not always hold. For example,

1. if A and B are two iron pieces and C is a magnet, then both A and B will be attracted by C, but A and B will not attract each other.
2. When each of two straight lines is per¬pendicular to a third straight line, the first two are not neces¬sarily perpendicular to each other.

Thus, we can understand that zeroth law is not an obvious truth, but has been formulated as a ‘law’ on the basis of experiments and experiences.

Analogical examples of the zeroth law:

1. a, b and c are three line segments. Out of these lines, if a is equal to c and b is also equal to c, we know from our experience that a and b are equal to each other.

There exists a property whose value is the same for all three line segments. This property is the length of a line segment. Hence, equality in length is the condition for the three line segments to be equal.

2. a, b, and c are three straight lines on a plane. a is parallel to c and b is also parallel to c. We know that a and b will also be parallel to each other, a, b, and c must have the same gradient or slope, and thus, equality in slope is the condition for the lines a, b, and c to be parallel to one another.

Significance Of The Zeroth law: From the analogies discussed above, it can be concluded that there must exist a characteristic property of every body, whose equality dictates thermal equilibrium among the bodies. This characteristic property is the temperature of a body.

Significance Of The Zeroth Law Definition: Temperature is a physical property of everybody, whose equality is the necessary and sufficient condition for thermal equilibrium among the bodies.

According to this definition,

1. All substances kept in a room for a long time are at the same temperature,
2. Temperature of hot water is different from that of cold water,
3. A hot body and a cold body, kept in thermal contact, attain the same temperature after some time, etc.

Properties Of Bulk Matter – Thermometer

An instrument that measures the temperature of a body is called a thermometer.

From zeroth law we see that, to determine the thermal equilibrium between A and B, a third body C can be used as a reference body. In this case C acts as a thermometer.

Temperature scale: A scale of temperature is needed to measure the temperature of a body accurately. To draw up a scale we follow the norm that a hot body is at a higher temperature while a cold body is at a lower temperature.

It implies that when a hot and a cold body are in contact, the temperature of the hot body will decrease and that of the cold body will increase. When the temperatures of both bodies become equal, the bodies attain thermal equilibrium.

Fixed point: To set up a temperature scale, one or more conveniently reproducible, well-established temperatures are chosen as standard temperatures. These fixed tempera¬tures are called the fixed points.

Primary thermometer: There are several kinds of thermometers for practical use. There are liquid thermometers (mercury or alcohol), ideal gas thermometers, platinum-resis-tance thermometers etc. Among these, there is a special kind of thermometer that is used to deduce the accurate value of different fixed points.

• This is known as a primary thermometer. Using these fixed points, other thermometers are calibrated. The universally accepted primary thermometer is the ideal gas thermometer.
• The thermometer contains a gas, under ideal conditions, kept at a constant volume. The property of the gas, that changes with temperature, is its pressure.

As such, pressure is called the thermometric property of the gas. The thermometer is also known as a constant-volume gas thermometer. To fix the ideal gas temperature scale, the temperature (T) is assumed to be proportional to the pres¬sure (p) of the gas. So,

T ∝ p, or, T = kp, where k is an unknown constant.

• To know the value of k, one fixed point should be chosen and its temperature allotted with a definite value. This fixed point, known as the fundamental fixed point, is the triple point of water (discussed below).
• The value of its temperature is universally accepted as 273.16. Later, Kelvin introduced a thermodynamic temperature scale, which exactly coincides with the ideal gas scale.

So the unit of temperature is chosen as kelvin or K; then the temperature of the triple point of water is T₀ = 273.16 K.

Triple point of water: The triple point of water is the state at which ice, water, and water vapour can coexist in thermal equilibirum. At this state, the pressure and the temperature are fixed so it is a fixed point.

• The value of pressure at this fixed point is 4.58 mm of Hg the value of temperature is assigned as 273.16 K in the ideal gas scale (see the chapter ‘Change of State of Matter’).
• Unless a very accurate value of temperature is required, we may use the number 273 in place of 273.16 for the triple point of water. In that case, C = K – 273; so practically there is no difference between the values of the triple point of water and ice point (see the table below).

Ideal gas scale: Scaling of the ideal gas thermometer is done considering the triple point of water as 273.16. Then temperatures of a few more fixed points are measured using this scale. The scale obtained from this is called ideal gas scale. Nowadays, Kelvin (K) is used as the unit instead of degree kelvin in ideal gas scale.

The following table lists some of the important fixed points and their temperatures measured and ascertained by an ideal gas thermometer. All fixed points other than the triple point of water are called secondary fixed points.

Secondary thermometer: All thermometers, other than the ideal gas thermometer, are secondary thermome¬ters. They are called secondary because they are calibrated according to the values of temperatures of fixed points already determined by an ideal gas thermometer.

• So all secondary thermometers actually obey the ideal gas temperature scale. However, it should be noted that secondary thermometers should never be regarded as less reliable or less efficient.
• Rather, they are often highly accurate and very easy to use. The most important of them are liquid ther¬mometer and resistance thermometer.

The four scales of temperature—Celcius, Fahrenheit, Reaumur, and Kelvin Fixed points and symbols:

Equivalence of the temperatures recorded in the four different scales mentioned above: Let C, F, R, and K be the temperature of a body as recorded in three different scales viz., Celsius, Fahrenheit, Reaumur, and Kelvin respectively. Then,

⇒ \(\frac{C-0}{100-0}=\frac{F-32}{212-32}=\frac{R-0}{80-0}=\frac{K-273}{373-273}\)

or, \(\frac{C}{5}=\frac{F-32}{9}=\frac{R}{4}=\frac{K-273}{5}\)

Equivalence of the temperature recorded in any two different scales: Let the temperature of a body in scale A be p and that in scale B be q. Then,

⇒ \(\frac{p \text {-lower fixed point in scale } A}{\text { upper fixed point in } A \text {-lower fixed point in } A}\)

= \(\frac{q \text {-lower fixed point in scale } B}{\text { upper fixed point in } B \text {-lower fixed point in } B}\)

 Properties Of Bulk Matter Heat

Heat Definition: The energy transferred from one body to another only because of a difference in temperature 1 between them is called heat.

Heat Discussion:

• It is to be noted that in thermodynamics, temperature has been define, first. Then heat energy is defined based on the difference in temperature.
• Hence, a statement like, “Heat is the cause and temperature is the effect” is not applicable in thermodynamics. In fact, there is no real need for such a simplification.
• The accepted convention for the direction of flow of heat is that, it flows from a body at a higher temperature to a body at a lower temperature.
• The statement, ‘only because of a difference in tempera-ture’, has been used in the definition of heat because difference in other physical properties, between two bodies may cause a flow of other forms of energy. For example, a difference in pressure between two bodies brought in contact causes the transfer of mechanical energy.
• While temperature is an intrinsic property of a body, ‘heat’ is not ‘Heat of a body’ is a meaningless concept. Heat energy manifests itself only when it is transferred from one body to another.
• Hence, heat is energy in transit. The statement, ‘temperature of a body is 20 °C ’, is meaningful. But the ‘heat of a body is 200 cal ’ is meaningless. Instead ‘heat transferred from A to B is 200 cal ’ is a correct statement.
• The amount of heat contained in a body can never be measured. What we measure in calorimetry is the amount of heat absorbed or liberated by a body not the ‘heat content’ of the body.

Thermal equilibrium: When two or more bodies are in thermal contact and the temperature of every one of them is the same, then no heat is exchanged among them. This state is called thermal equilibrium.

Unit 7 Properties Of Bulk Matter Chapter 4 Thermometry Heat Numerical Examples

Example 1. What is the temperature which has the same value in Celsius and in Fahrenheit scales?
Solution:

The temperature which has the same value in Celsius and in Fahrenheit scales

Let the temperature be x degree. As per the question C = F = x

From the relation for equivalence of temperature scales, we
know \(\frac{C}{5}=\frac{F-32}{9}\)

∴ \(\frac{x}{5}=\frac{x-32}{9}\) or, 9x = 5x- 160

or, 4x = -160

∴ x = -40

∴ -40 °C = -40 °F

Example 2. A thermometer has its lower fixed point and upper fixed point marked as 0.5 and 101 respectively. What is the reading on this thermometer at 30 °C?
Solution:

A thermometer has its lower fixed point and upper fixed point marked as 0.5 and 101 respectively.

Let the reading be t degree.

∴ \(\frac{t-0.5}{101-0.5}=\frac{C}{100} \text { or, } \frac{t-0.5}{100.5}=\frac{30}{100}\)

or, 10t-5 = 301.5 or, t = 30.65 degree

Hence, the faulty thermometer reads 30.65 degree.

Example 3. A faulty thermometer reads -0.5 °C in melting ice and 99 °C in boiling water at the pressure of 747 mm of Hg. What is the correct temperature when the faulty thermometer reads 45 °C? The actual boiling point of water is 99 °C at 734 mm of Hg.
Solution:

A faulty thermometer reads -0.5 °C in melting ice and 99 °C in boiling water at the pressure of 747 mm of Hg.

Actual boiling point of water at the pressure of 760 mm of Hg is 100 °C.

Now, a decrease in pressure by (760 – 734) or 26 mm of Hg decreases the boiling point of water by (100 – 99) = 1 °C.

∴ The decrease in pressure by (760-747) or, 13 mm of Hg decreases the boiling point of water by 1/26 x 13 = 0.5 °C.

Hence, the boiling point of water at 747 mm of Hg should be (100-0.5) = 99.5 °C.

Let the correct temperature be x °C, when the faulty ther-mometer reads 45 °C.

Hence, \(\frac{x}{99.5}=\frac{45-(-0.5)}{99-(-0.5)}=\frac{45.5}{99.5} \quad therefore x=45.5^{\circ} \mathrm{C} \text {. }\)

Temperature of the freezing mixture = -23°C

Example 4. A centimetre scale is attached with a thermometer of uniform bore. The thermometer reads 7.3 cm in melting ice, 23.8 cm in boiling water and 3.5 cm in a freezing mixture. What is the temperature of this freezing mixture in °C?
Solution:

A centimetre scale is attached with a thermometer of uniform bore. The thermometer reads 7.3 cm in melting ice, 23.8 cm in boiling water and 3.5 cm in a freezing mixture.

The lower and the upper fixed points correspond to readings of 7.3 cm and 23.8 cm respectively. The tem­perature of the freezing mixture in this scale corresponds to a scale reading of 3.5 cm.

Let C be the freezing mixture’s temperature in degree Cel­sius.

Temperature of the freezing mixture = – 23.03 °C.

Alternative solution: When the temperature increases from 0 °C to 100 °C, the corresponding change in scale reading = 23.8 – 7.3 = 16.5 cm.

So when the temperature changes by 1 °C, the corresponding changes in scale reading = 16.85/100 = 0.165 cm

Let the temperature of the freezing mixture =-x °C

So change in temperature in Celcius scale = 0 – (-x) = x °C

The corresponding change in scale reading = 0.165x cm.

According to the question,

0. 165X = 7.3-3.5 or, x = 38/0.165 = 23.03

So the temperature of the freezing mixture is -23.03 °C.

Example 5. A substance is heated from 30 °C to 75 °C. What is the change in its temperature on the Fahrenheit scale and on the Kelvin scale?
Solution:

A substance is heated from 30 °C to 75 °C.

Let a temperature be C on the Celsius scale, F on the Fahrenheit scale and T on the Kelvin scale. We can write,

F = 9/5C + 32 ….(1)

and T = C+273 ….(2)

Differentiating equation (1) we get,

⇒ \(\Delta F=\frac{9}{5} \Delta C\)

Here, ΔC = 75 – 30 = 45

∴ ΔF = 9/5 x 45 = 81.

Similarly, by differentiating equation (2) we get, ΔT = ΔC = 45.

Example 6. The graph between Celcius and Fahrenheit temperature of a body is shown. Show that the angle made by the graph with Celsius axis is \(\sin ^{-1} \frac{9}{\sqrt{106}}\)

Solution:

The graph between Celcius and Fahrenheit temperature of a body is shown.

We know, \(\frac{C}{5}=\frac{F-32}{9} \text { or, } C=\frac{5}{9}(F-32) \text { or, } F=\frac{9}{5} C+32\)

This is the equation of a straight line, Here the slope of the line, tanθ = 9/5

∴ OA = \(\sqrt{5^2+9^2}=\sqrt{106}\)

∴ \(\sin \theta=\frac{9}{\sqrt{106}}\)

or, \(\theta=\sin ^{-1} \frac{9}{\sqrt{106}}\)

 

Unit 7 Properties Of Bulk Matter Chapter 4 Thermometry Synopsis

Zeroth law of thermodynamics: If two bodies are separately, in thermal equilibrium with a third body, then the first two bodies are also in thermal equilibrium with each other.

• Temperature is a physical property of any system, whose equality indicates thermal equilibrium between different systems.
• The instrument that measures the temperature of a body is called a thermometer.
• The energy transferred from one body to another due to the difference of temperature only is called heat.
• Thermal equilibrium: When two or more bodies are in thermal contact and the temperature of each body is the same, then no heat is exchanged among them. This state is called thermal equilibrium.

Unit 7 Properties Of Bulk Matter Chapter 4 Thermometry Useful Relations For Solving Numerical Problems

If any temperature in Celsius, Fahrenheit and Kelvin scales be C, F and K respectively, then

⇒ \(\frac{C}{5}=\frac{F-32}{9}=\frac{K-273}{5}\)

Relation of temperature readings in any two scales: If any temperature on one scale be p and that on some other scale be q then,

⇒ \(\frac{p-\text { lower fixed point in the first scale }}{\text { upper fixed point in that scale }- \text { lower fixed point in that scale }}\)

= \(\frac{q-\text { lower fixed point in the second scale }}{\text { upper fixed point in that scale }- \text { lower fixed point in that scale }}\)

Unit 7 Properties Of Bulk Matter Chapter 4 Thermometry Match Column 1 And Column 2

Question 1. Ranges of different thermometers are given below.

Answer: 1. 3, 2. D, 3. B, 4. A

Unit 7 Properties Of Bulk Matter Chapter 4 Thermometry Comprehension Type Questions

Read the following passage carefully and answer the questions at the end of it.

Question 1. Perhaps the highest temperature material you will ever see is the sun’s outer atmosphere or corona. At a temperature of about 2 x 10⁶ °C or 3.6 x 10⁶ °F, the corona glows with a light that is literally unearthly. But because corona is also very thin, its light is rather faint. You can only see the corona during a total solar eclipse when the sun’s disk is covered by the moon.

1. Is it accurate to say that the corona contains heat?

1. Yes
2. No
3. In particular, conditions, say during solar eclipse, it contain heat
4. None of these

Answer: 1. Yes

2. What is the highest temperature which can be created on earth for a sufficiently long time?

1. 1500°C
2. 2000°C
3. 2500°C
4. 3000 K

Answer: 4. 3000 K

3. To measure high temperatures > 2500°C we use

1. Constant volume gas thermometer
2. Thermocouple
3. Resistance thermometer
4. Pyrometer

Answer: 4. Pyrometer

Unit 7 Properties Of Bulk Matter Chapter 4 Thermometry Integer Type Questions

In these type, the answer to each of the questions is a single-digit integer ranging from 0 to 9.

1. A Celsius and a Fahrenheit thermometer are put in a hot bath. The reading of the Fahrenheit thermometer is just 29/5 times the reading on the Celsius thermometer. What is the temperature of the bath in Celsius?
Answer: 8