## Unit 9 Behavior Of Perfect Gas And Kinetic Theory Chapter 1 Kinetic Theory Of Gases Multiple Choice Questions And Answers

**Question 1. If the volume of a body is V _{1 }and the total volume of the molecules of the body is V_{2}, then**

- V
_{1}= V_{2} - V
_{1 }< V_{2} - V
_{1 }>V_{2} - V
_{1}< V_{2}or V_{1}> V_{2}for different bodies

**Answer:** 3. V_{1 }>V_{2}

**Question 2. The molecules of all solids**

- Are relatively closer than those of liquids or gases
- Are relatively farther than those of liquids or gases
- Move faster than those of liquids or gases
- Are stationary as they cannot move inside the solid

**Answer:** 1. Are relatively closer than those of liquids or gases

**Question 3. Which of the following statements is inconsistent with the characteristics of Brownian motion?**

- The velocity of a particle increases as its size decreases
- The velocity of the particles increases as the temperature increases
- The velocity of the particles increases as the viscosity of the medium decreases
- The velocity of the particles increases when the container is shaken

**Answer:** 4. The velocity of the particles increases when the container is shaken

**Question 4. A piece of wood floating on water does not have any Brownian motion, because**

- A part of the wooden piece is above the water
- The resultant of the applied forces by the water molecules is zero
- An adhesive force acts between the molecules of wood and water
- The viscosity of water is comparatively less

**Answer:** 2. The resultant of the applied forces by the water molecules is zero

**Question 5. The velocities of two particles moving towards the east are 4 m · s ^{-1} and 6 m · s^{-1}, respectively. The velocities of three other particles moving towards the west are 2 m · s^{-1}, 3 m · s^{-1}, and 5 m · s^{-1}, respectively. The root mean square speed of these 5 particles is**

- 0
- 4m · s
^{-1} - 1.667 m · s
^{-1} - 4.242 m · s
^{-1}

**Answer:** 4. 4.242 m · s^{-1}

**Question 6. The pressure and density of hydrogen gas, kept in a vessel, are 1.013 x 10 ^{6} dyn · cm^{-2} and 0.089 g · L^{-1}, respectively. The rms speed of the gas molecules will be**

- 18.5m · s
^{-1} - 185m · s
^{-1} - 1.85 km · s
^{-1} - 18.5 km · s
^{-1}

**Answer:** 3. 1.85 km · s^{-1}

**Question 7. If the mean velocity, rms speed, and maximum probable velocity of gas are c, c, and cm, respectively, then**

- \(c_m<\bar{c}<c\)
- \(\bar{c}<c<c_m\)
- \(c_m>\bar{c}>c\)
- None of these

**Answer:** 1. \(c_m<\bar{c}<c\)

**Question 8. There is a mixture of hydrogen and oxygen gases in a vessel. The root mean square speed of the oxygen molecules is**

- 4 times that of hydrogen molecules
- 16 times that of hydrogen molecules
- 1/4 times that of hydrogen molecules
- 1/16 times that of hydrogen molecules

**Answer:** 3. 1/4 times that of hydrogen molecules

**Question 9. A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds is**

- 0.32
- 0.45
- 2.24
- 3.16

**Answer:** 4. 3.16

**Question 10. At room temperature, the rms speed of the molecules of a certain diatomic gas is found to be 1930 m/s. The gas is**

- H
_{2} - F
_{2} - O
_{2} - Cl
_{2}

**Answer:** 1. H_{2}

**Question 11. If the volume of a container is V, the pressure on the walls of the container by a gas is p and the internal energy of the gas is U, then**

- U = p V
- U = \(\frac{1}{3} p V\)
- U = \(\frac{2}{3} p V\)
- U = \(\frac{3}{2} p V\)

**Answer:** 4. U = \(\frac{3}{2} p V\)

**Question 12. A certain amount of gas is at 27°C. The rms speed of the gas molecules becomes doubled at**

- 327°C
- 600°C
- 927°C
- 1200°C

**Answer:** 3. 1200°C

**Question 13. If a gas of a particular mass is expanded at a constant temperature, the variable which undergoes a change is**

- Pressure of the gas
- Internal energy of the gas
- Rms speed of the gas molecules
- Kinetic energy of the gas molecules

**Answer:** 1. Pressure of the gas

**Question 14. At equilibrium conditions, the volume, pressure, and temperature of a gas kept in a closed container are V, p, and T, respectively. If the container is divided into two equal parts by a partition, the value of these quantities for each part will be**

- \(\frac{V}{2}, \frac{p}{2}, \frac{T}{2}\)
- \(\frac{V}{2}, \frac{p}{2}, T\)
- \(\frac{V}{2}, p, \frac{T}{2}\)
- \(\frac{V}{2}, p, T\)

**Answer:** 4. \(\frac{V}{2}, p, T\)

**Question 15. According to the kinetic theory of gases, there are no intermolecular attractions, so these molecules do not have**

- Linear momentum
- Kinetic energy
- Potential energy
- Mechanical energy

**Answer:** 3. Linear momentum

**Question 16. If k is Boltzmann constant and T is temperature, the average kinetic energy of each molecule of a gas will be**

- \(\frac{2}{3} k T\)
- \(\sqrt{\frac{2}{3}} k T\)
- \(\frac{3}{2} k T\)
- \(\sqrt{\frac{3}{2}} k T\)

**Answer:** 3. \(\frac{3}{2} k T\)

**Question 17. The rms speed of oxygen molecules at 47°C will be equal to the rms speed of hydrogen molecules at**

- 80K
- -83K
- 3K
- 20K

**Answer:** 4. 20K

**Question 18. The pressure, volume, and temperature in two samples of a gas are p, V, T, and 2p,V/4, 2 T, respectively The ratio of the number of molecules in the two samples is**

- 2:1
- 4:1
- 8:1
- 16:1

**Answer:** 2. 4:1

**Question 19. The rms speed of gas molecules at 0°C will be reduced to half at**

- 0°C
- -273°C
- 32°C
- -204°C

**Answer:** 4. -204°C

**Question 20. A container of 5 L contains 10 ^{26} number of molecules of a gas. If the mass and rms speed of each molecule are 2.4 x 10^{-25 }g and 3.5 x 10^{4} cm · s^{-1}, respectively the pressure of the gas will approximately be**

- 2 x 10
^{6}dyn · cm^{-2} - 10
^{6}dyn · cm^{-2} - 3 x 10
^{6}dyn · cm^{-2} - 5 x 10
^{6}dyn · cm^{-2}

**Answer:** 1. 2 x 10^{6} dyn · cm^{-2}

**Question 21. Air is filled in two heat-insulated vessels 1 and 2 having pressure, volume, and temperature p _{1}, V_{1}, T_{1} and p_{2}, V_{2}, T_{2} respectively. If the intermediate valve between the two vessels is opened, the temperature of the air at equilibrium will be**

- \(T_1+T_2\)
- \(\frac{T_1 T_2\left(p_1 V_1+p_2 V_2\right)}{p_1 V_1 T_2+p_2 V_2 T_1}\)
- \(\frac{T_1+T_2}{2}\)
- \(\frac{T_1 T_2\left(p_1 V_1+p_2 V_2\right)}{p_1 V_1 T_1+p_2 V_2 T_2}\)

**Answer:** 3. \(\frac{T_1+T_2}{2}\)

**Question 22. A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at 300 K. The ratio of the average rotational kinetic energy per O _{2 }molecule to per N_{2} molecule is**

- 1:1
- 1:2
- 2:1
- Depends on the moment of inertia of the two molecules

**Answer:** 1. 1:1

**Question 23. 70 cal of heat is required to raise the temperature of 20 moles of an ideal diatomic gas at constant pressure from 30°C. The amount of heat required (in cal) to raise the temperature of the same gas through the same range (30°C to 35°C) at constant volume is**

- 30
- 50
- 70
- 90

**Answer:** 2. 50

**Question 24. Three closed vessels A, B, and C at the same temperature T contain gases that obey the Maxwellian distribution of velocities. Vessel A contains only O _{2}, B only N_{2}, and C a mixture of equal quantities of O_{2} and N_{2}. If the average velocity of the O_{2} molecule in vessel A is v_{2} and that of the N_{2} molecule in vessel B is v_{2}, the average velocity of the O_{2} molecule is vessel C is**

- \(\frac{\left(v_1+v_2\right)}{2}\)
- \(v_1\)
- \(\left(v_1 \nu_2\right)^{\frac{1}{2}}\)
- \(\sqrt{\frac{3 k T}{M}}\)

**Answer:** 2. \(v_1\)

**In this type of question, more than one option are correct**

**Question 25. From the following statements concerning ideal gas at any given temperature T, select the correct one(s).**

- The coefficient of volume expansion at constant pressure is the same for all ideal gases
- The average translational kinetic energy per molecule of oxygen gas is 3kT, k being the Boltzmann constant
- The mean free path of molecules increases with a decrease in pressure
- In a gaseous mixture, the average translational kinetic energy of the molecules of each component

**Answer:**

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

3. The mean free path of molecules increases with a decrease in pressure

**Question 26. Let \(\bar{v}, v_{\mathrm{rms}} \text { and } v_p\) respectively, denote the mean velocity, root mean square speed, and most probable velocity of the molecules in an feed monatomic gas at absolute temperature T. The mass of a molecule is m. Then**

- No molecule can have a speed greater than \(\sqrt{2} v_{\mathrm{rms}}\)
- No molecule can have speed less than \(\frac{v_p}{\sqrt{2}}\)
- \(v_p<\bar{v}<v_{\mathrm{rms}}\)
- The average kinetic energy of a molecule is \(\frac{3}{4} m v_p^2\)

**Answer:**

3. \(v_p<\bar{v}<v_{\mathrm{rms}}\)

4. The average kinetic energy of a molecule is \(\frac{3}{4} m v_p^2\)

**Question 27. For a jar containing H _{2} gases which of the following statements are correct?**

- Both the gas molecules have same average energy
- Both the gas molecules have same average translational kinetic energy
- Hydrogen molecules have greater average energy than helium molecules
- Both the molecules have same average velocity

**Answer:**

3. Hydrogen molecules have greater average energy than helium molecules

4. Both the molecules have same average velocity

**Question 28. The root mean square speed of the perfect gas molecules will be doubled if**

- Pressure is doubled at constant volume
- Pressure is made 4 times at constant volume
- Volume is made 4 times at constant pressure
- Volume is increased by 41.4% at constant pressure

**Answer:**

2. Pressure is made 4 times at constant volume

3. Volume is made 4 times at constant pressure

**Question 29. According to the kinetic theory of gases, which of the following statements are true?**

- Real gas behaves as ideal gas at high temperatures and low pressure
- The liquid state of an ideal gas is impossible
- At any temperature and pressure, ideal gas obeys Boyle’s law and Charles’ law
- The molecules of a real gas do not exert any force on one another

**Answer:**

- Real gas behaves as ideal gas at high temperatures and low pressure
- The liquid state of an ideal gas is impossible
- At any temperature and pressure, ideal gas obeys Boyle’s law and Charles’ law