Kinetic Theory of Gases · JEE Main previous year questions

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound, then the value of n will be :

1. A.1
2. B.2
3. C.3
4. D.4

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

1. A.The velocity of atomic oxygen remains same
2. B.The velocity of atomic oxygen doubles
3. C.The velocity of atomic oxygen becomes half
4. D.The velocity of atomic oxygen becomes four times

According to kinetic theory of gases, A. The motion of the gas molecules freezes at $0^{\circ }\text{C}$. B. The mean free path of gas molecules decreases if the density of molecules is increased. C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant. D. Average kinetic energy per molecule per degree of freedom is $\frac{3}{2}{k}_{B}T$ (for monoatomic gases). Choose the most appropriate answer from the options given below :

1. A.A and C only
2. B.B and C only
3. C.A and B only
4. D.C and D only

The relation between root mean square speed ($v_{\mathrm{rms}}$) and most probable speed ($v_{\mathrm{p}}$) for the molar mass $\mathrm{M}$ of oxygen gas molecule at the temperature of $300\text{ K}$ will be :

1. A.$v_{\mathrm{rms}}=\sqrt{\frac{2}{3}}{v}_{\mathrm{p}}$
2. B.$v_{\mathrm{rms}}=\sqrt{\frac{3}{2}}{v}_{\mathrm{p}}$
3. C.$v_{\mathrm{rms}}=v_{\mathrm{p}}$
4. D.$v_{\mathrm{rms}}=\sqrt{\frac{1}{3}}{v}_{\mathrm{p}}$

The amount of heat needed to raise the temperature of 4 moles of rigid diatomic gas from $0^{\circ }\text{ C}$ to $50^{\circ }\text{ C}$ when no work is done is ________. (R is the universal gas constant).

1. A.$500\text{ R}$
2. B.$250\text{ R}$
3. C.$750\text{ R}$
4. D.$175\text{ R}$

What will be the average value of energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature T? ($k_{\mathrm{B}}$ is Boltzmann constant)

1. A.$\frac{1}{2}{k}_{\mathrm{B}}T$
2. B.$\frac{2}{3}{k}_{\mathrm{B}}T$
3. C.$\frac{3}{2}{k}_{\mathrm{B}}T$
4. D.$k_{\mathrm{B}}T$

1. A.$\sqrt{\frac{3\pi }{8}}$
2. B.$\sqrt{\frac{\sqrt{3}}{3}}$
3. C.$\sqrt{\frac{8}{3}}$
4. D.$\sqrt{\frac{8\pi }{3}}$

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of $\gamma \left(=\frac{C_p}{C_v}\right)$ are given, respectively by:

1. A.$U=\frac{5}{2}RT$ and $\gamma =\frac{7}{5}$
2. B.$U=5RT$ and $\gamma =\frac{6}{5}$
3. C.$U=5RT$ and $\gamma =\frac{7}{5}$
4. D.$U=\frac{5}{2}RT$ and $\gamma =\frac{6}{5}$

To raise the temperature of a certain mass of gas by $50^{\circ }\mathrm{C}$ at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by $100^{\circ }\mathrm{C}$ at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

1. A.6
2. B.7
3. C.5
4. D.3

An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true? (A) the mean free path of the molecules decreases. (B) the mean collision time between the molecules decreases. (C) the mean free path remains unchanged. (D) the mean collision time remains unchanged.

1. A.(C) and (D)
2. B.(A) and (D)
3. C.(B) and (C)
4. D.(A) and (B)

Two moles of an ideal gas with $\frac{C_p}{C_v}=\frac{5}{3}$ are mixed with 3 moles of another ideal gas with $\frac{C_p}{C_v}=\frac{4}{3}$. The value of $\frac{C_p}{C_v}$ for the mixture is :

1. A.1.50
2. B.1.45
3. C.1.47
4. D.1.42

For a given gas at 1 atm pressure, rms speed of the molecule is 200 m/s at 127°C. At 2 atm pressure and at 227°C, the rms speed of the molecules will be :

1. A.100 m/s
2. B.$100\sqrt{5}$ m/s
3. C.$80\sqrt{5}$ m/s
4. D.80 m/s

A mixture of 2 moles of helium gas (atomic mass = $4\text{ u}$), and 1 mole of argon gas (atomic mass = $40\text{ u}$) is kept at $300\text{ K}$ in a container. The ratio of their rms speeds $\left[\frac{V_{\mathrm{rms}}(\text{helium})}{V_{\mathrm{rms}}(\text{argon})}\right]$, is close to :

1. A.3.16
2. B.0.32
3. C.0.45
4. D.2.24

1. A.
2. B.
3. C.
4. D.

1. A.$\frac{9P_0{V}_0}{2nR}$
2. B.$\frac{9P_0{V}_0}{nR}$
3. C.$\frac{9P_0{V}_0}{4nR}$
4. D.$\frac{3P_0{V}_0}{2nR}$

1. A.$\frac{9P_0{V}_0}{nR}$
2. B.$\frac{3P_0{V}_0}{2nR}$
3. C.$\frac{9P_0{V}_0}{2nR}$
4. D.$\frac{9P_0{V}_0}{4nR}$

Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

1. A.increase
2. B.decrease
3. C.remain same
4. D.decrease for some, while increase for others