Kinetic Theory of Gases JEE Advanced previous year questions with solutions

5 solved JEE Advanced questions on Kinetic Theory of Gases, free to read — no sign-in needed. The full chapter has 6 questions; sign in to attempt the remaining 1 in the exam simulator.

1. Q1JEE Advanced Adv 2015 (Paper 1)
   A container of fixed volume has a mixture of one mole of hydrogen and one mole of helium in equilibrium at temperature $T$ . Assuming the gases are ideal, the correct statement(s) is (are)
   1. A.The average energy per mole of the gas mixture is $2RT$
   2. B.The ratio of speed of sound in the gas mixture to that in helium gas is $\sqrt{\dfrac{6}{5}}$
   3. C.The ratio of the rms speed of helium atoms to that of hydrogen molecules is $\dfrac{1}{2}$
   4. D.The ratio of the rms speed of helium atoms to that of hydrogen molecules is $\dfrac{1}{\sqrt{2}}$
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   Answer: A,B,D

   ${C}_{V\left(mix\right)}=\dfrac{\left(1\right)\left(\dfrac{3}{2}R\right)+\left(1\right)\left(\dfrac{5}{2}R\right)}{2}=2R$ ${C}_{P\left(mix\right)}=3R$ ${\gamma }_{mix}=\dfrac{3}{2}\Rightarrow f=4$ Average energy/mole $=f\dfrac{1}{2}RT=2RT$ $\dfrac{{\left({V}_{sound}\right)}_{mixture}}{{\left({V}_{sound}\right)}_{He}}=\dfrac{\sqrt{\dfrac{RT}{2}}}{\sqrt{\dfrac{5RT}{12}}}=\sqrt{\dfrac{6}{5}}$ $\dfrac{{\left({V}_{rm}\right)}_{He}}{{\left({V}_{rms}\right)}_{{H}_{2}}}=\dfrac{\sqrt{\dfrac{3RT}{4}}}{\sqrt{\dfrac{3RT}{2}}}=\dfrac{1}{\sqrt{2}}$
2. Q2JEE Advanced Adv 2013 (Paper 1)
   Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their densities is
   1. A.1 : 4
   2. B.1 : 2
   3. C.6 : 9
   4. D.8 : 9
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   Answer: (D)

   Given, $\dfrac{{\text{m}}_{\text{A}}}{{\text{m}}_{\text{B}}}=\dfrac{2}{3 ​}$ $∵$ Volume and temperature is same. From ideal gas equation, $PV=nRT$ $\dfrac{\text{P}}{\text{n}}=constant$ $\dfrac{{\text{P}}_{\text{A}}}{{\text{n}}_{\text{A}}}=\dfrac{{\text{P}}_{\text{B}}}{{\text{n}}_{\text{B}}}\Rightarrow \dfrac{{\text{n}}_{\text{A}}}{{\text{n}}_{\text{B}}}=\dfrac{{\text{P}}_{\text{A}}}{{\text{P}}_{\text{B}}}=\dfrac{4}{3}$ Also, density, $\rho =\dfrac{M}{V}$ $\dfrac{{\text{ρ}}_{\text{A}}}{{\text{ρ}}_{\text{B}}}=\dfrac{{\text{M}}_{\text{A}}/\text{v}}{{\text{M}}_{\text{B}}/\text{v}}=\dfrac{{\text{n}}_{\text{A}}{m}_{\text{A}}}{{\text{n}}_{\text{B}}{\text{m}}_{\text{B}}}$ $=\dfrac{4}{3}\times \dfrac{2}{3}=\dfrac{8}{9}$.
3. Q3JEE Advanced Adv 2012 (Paper 1)
   A mixture of 2 moles of helium gas (atomic mass $=4 \mathrm{amu}$ ) and 1 mole of argon gas (atomic mass $=40 \mathrm{amu}$ ) is kept at $300 \mathrm{~K}$ in a container. The ratio of the rms speeds $\left(\frac{v_{\mathrm{rms}}(\text { helium })}{v_{\mathrm{rms}}(\operatorname{argon})}\right)$ is
   1. A.$0.32$
   2. B.$0.45$
   3. C.$2.24$
   4. D.$3.16$
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   Answer: (D)

   Using $V_{\mathrm{rms}}=\sqrt{\frac{3 R T}{M}} \Rightarrow V_{r m s} \propto \frac{1}{\sqrt{M}}$ $\frac{v_{\text {rms (helium) }}}{v_{\text {rms (argon) }}}=\sqrt{\frac{M_{\text {argon }}}{M_{\text {helium }}}}=\sqrt{\frac{40}{4}}=\sqrt{10} \approx 3.16$
4. Q4JEE Advanced Adv 2010 (Paper 1)
   A real gas behaves like an ideal gas if its
   1. A.pressure and temperature are both high
   2. B.pressure and temperature are both low
   3. C.pressure is high and temperature is low
   4. D.pressure is low and temperature is high
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   Answer: (D)

   A real gas behaves like an ideal gas at low pressure and high temperature. $\therefore$ correct option is (d).
5. Q5JEE Advanced Adv 2009 (Paper 1)
   $C_V$ and $C_p$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then
   1. A.$C_p-C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
   2. B.$C_p+C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.
   3. C.$\frac{C_p}{C_V}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
   4. D.$C_p \cdot C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas
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   Answer: B,D

   For monoatomic gas, $$C_p=\frac{5}{2} R \text { and } C_V=\frac{3}{2} R$$ For diatomic gas, $$C_p=\frac{7}{2} R \text { and } C_V=\frac{5}{2} R$$