Unit – 9 : Kinetic Theory of Gases (Multiple Choice Questions)

1. A particle of mass $m$ moves with speed $u$ making $60^\circ$ with x-axis and undergoes elastic collision with a wall. The change in momentum is

Elastic collision of particle with wall
a) $\Delta p_x=-mu,\ \Delta p_y=0$
b) $\Delta p_x=-2mu,\ \Delta p_y=0$
c) $\Delta p_x=0,\ \Delta p_y=mu$
d) $\Delta p_x=mu,\ \Delta p_y=0$
Answer: a)

2. A sample of ideal gas is in equilibrium. Which of the following is zero?

a) rms speed
b) average speed
c) average velocity
d) most probable speed
Answer: c)

3. An ideal gas is kept at constant pressure. If temperature increases from 100 K to 1000 K, the rms speed

a) increases 5 times
b) increases 10 times
c) remains same
d) increases 7 times
Answer: b)

4. Two identical rooms A and B are connected by an open door. Room A is air-conditioned and its temperature is 4°C less than room B. Which room has more air?

a) Room A
b) Room B
c) Both have same air
d) Cannot be determined
Answer: a)

5. The average translational kinetic energy of gas molecules depends on

a) number of moles and $T$
b) only on $T$
c) $P$ and $T$
d) $P$ only
Answer: b)

6. If internal energy $U$ and volume $V$ of an ideal gas are doubled, then pressure

a) doubles
b) remains same
c) halves
d) quadruples
Answer: b)

7. The ratio $\dfrac{C_p}{C_v}$ for a gas mixture consisting of 8 g helium and 16 g oxygen is

a) 23/15
b) 15/23
c) 27/17
d) 17/27
Answer: c)

8. A container has one mole of monoatomic ideal gas. Each molecule has $f$ degrees of freedom. The ratio $\gamma=\dfrac{C_p}{C_v}$ is

a) $f$
b) $\dfrac{f}{2}$
c) $\dfrac{f}{f+2}$
d) $\dfrac{f+2}{f}$
Answer: d)

9. If temperature and pressure of a gas are doubled, the mean free path of molecules

a) remains same
b) doubled
c) tripled
d) quadrupled
Answer: a)

10. Which graph represents the correct relationship between pressure and density of an ideal gas at constant temperature?

Pressure vs density graphs
a) a
b) b
c) c
d) d
Answer: d)

11. A gas contains $\mu_1$ moles monoatomic, $\mu_2$ moles diatomic and $\mu_3$ moles triatomic molecules at high temperature. The total degrees of freedom is

a) $[3\mu_1+7(\mu_2+\mu_3)]N_A$
b) $[3\mu_1+7\mu_2+6\mu_3]N_A$
c) $[7\mu_1+3(\mu_2+\mu_3)]N_A$
d) $[3\mu_1+6(\mu_2+\mu_3)]N_A$
Answer: a)

12. If $s_p$ and $s_v$ are specific heats of nitrogen gas per unit mass at constant pressure and volume, then

a) $s_p-s_v=28R$
b) $s_p-s_v=\dfrac{R}{28}$
c) $s_p-s_v=\dfrac{R}{14}$
d) $s_p-s_v=R$
Answer: b)

13. Which gas has least rms speed at a given temperature?

a) Hydrogen
b) Nitrogen
c) Oxygen
d) Carbon dioxide
Answer: d)

14. For a gas molecule at fixed temperature, the area under Maxwell–Boltzmann distribution curve equals

a) $\dfrac{PV}{kT}$
b) $\dfrac{kT}{PV}$
c) $\dfrac{P}{NkT}$
d) $PV$
Answer: a)

15. The graph of pressure versus number density for an ideal gas at temperatures $T_1$ and $T_2$ implies

Pressure vs number density graph
a) $T_1=T_2$
b) $T_1>T_2$
c) $T_1 d) Cannot be determined
Answer: b)