Kinetic Theory of Gases · JEE Main previous year questions

2022 8 questions

1. Q472022 · 29 Jul 2022 · Shift 2

   The root mean square speed of smoke particles of mass $5\times 10^{-17}\mathrm{kg}$ in their Brownian motion in air at NTP is approximately. $[\text{Given }\mathrm{k}=1.38\times 10^{-23}\mathrm{J}{\mathrm{K}}^{-1}]$

   1. A.$60\mathrm{mm}{\mathrm{s}}^{-1}$
   2. B.$12\mathrm{mm}{\mathrm{s}}^{-1}$
   3. C.$15\mathrm{mm}{\mathrm{s}}^{-1}$
   4. D.$36\mathrm{mm}{\mathrm{s}}^{-1}$
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   Answer: C

2. Q372022 · 28 Jul 2022 · Shift 1

   Given below are two statements : Statement I : The average momentum of a molecule in a sample of an ideal gas depends on temperature. Statement II : The rms speed of oxygen molecules in a gas is $v$. If the temperature is doubled and the oxygen molecules dissociate into oxygen atoms, the rms speed will become $2v$. In the light of the above statements, choose the correct answer from the options given below :

   1. A.Both Statement I and Statement II are true
   2. B.Both Statement I and Statement II are false
   3. C.Statement I is true but Statement II is false
   4. D.Statement I is false but Statement II is true
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   Answer: D

3. Q542022 · 28 Jul 2022 · Shift 2· Numerical answer

   At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _________ J.

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   Answer: 750

4. Q382022 · 27 Jul 2022 · Shift 2

   Which statements are correct about degrees of freedom ? (A) A molecule with $\mathrm{n}$ degrees of freedom has ${\mathrm{n}}^2$ different ways of storing energy. (B) Each degree of freedom is associated with $\frac{1}{2}\mathrm{RT}$ average energy per mole. (C) A monatomic gas molecule has 1 rotational degree of freedom whereas diatomic molecule has 2 rotational degrees of freedom. (D) $\mathrm{C}{\mathrm{H}}_4$ has a total of 6 degrees of freedom. Choose the correct answer from the options given below :

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

5. Q422022 · 25 Jul 2022 · Shift 2

   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
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   Answer: B

6. Q392022 · 28 Jun 2022 · Shift 2

   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
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   Answer: B

7. Q382022 · 27 Jun 2022 · Shift 2

   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
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   Answer: B

8. Q372022 · 25 Jun 2022 · Shift 1

   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.$v_{\mathrm{rms}}=\sqrt{\frac{1}{3}}{v}_{\mathrm{p}}$
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   Answer: B