Kinetic Theory of Gases · JEE Main previous year questions

2023 9 questions

1. Q372023 · 13 Apr 2023 · Shift 1

   The rms speed of oxygen molecule in a vessel at particular temperature is ${\left(1+\frac{5}{x}\right)}^{\frac{1}{2}}v$, where $v$ is the average speed of the molecule. The value of $x$ will be: ( Take $\pi =\frac{22}{7}$ )

   1. A.$4$
   2. B.$8$
   3. C.$28$
   4. D.$27$
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   Answer: C

2. Q412023 · 13 Apr 2023 · Shift 2

   The mean free path of molecules of a certain gas at STP is $1500\text{ d}$, where $\mathrm{d}$ is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at $373\text{ K}$ is approximately:

   1. A.$750\text{ d}$
   2. B.$1500\text{ d}$
   3. C.$2049\text{ d}$
   4. D.$1098\text{ d}$
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   Answer: C

3. Q362023 · 11 Apr 2023 · Shift 1

   Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafluoride (polyatomic). Arrange these on the basis of their root mean square speed ($v_{\text{rms}}$) and choose the correct answer from the options given below:

   1. A.${\text{v}}_{\text{rms}}(\text{ mono })={\text{v}}_{\text{rms}}(\text{ dia })={\text{v}}_{\text{rms}}(\text{ poly })$
   2. B.${\text{v}}_{\text{rms}}(\text{mono})>{\text{v}}_{\text{rms}}(\text{dia})>{\text{v}}_{\text{rms}}(\text{poly})$
   3. C.${\text{v}}_{\text{rms}}(\text{dia})<{\text{v}}_{\text{rms}}(\text{poly})<{\text{v}}_{\text{rms}}(\text{mono})$
   4. D.${\text{v}}_{\text{rms}}(\text{mono})<{\text{v}}_{\text{rms}}(\text{dia})<{\text{v}}_{\text{rms}}(\text{poly})$
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   Answer: B

4. Q482023 · 11 Apr 2023 · Shift 2

   The root mean square speed of molecules of nitrogen gas at $27^{\circ }\mathrm{C}$ is approximately : (Given mass of a nitrogen molecule $=4.6\times 10^{-26}\text{ kg}$ and take Boltzmann constant $k_{\mathrm{B}}=1.4\times 10^{-23}{\text{ J K}}^{-1}$)

   1. A.$91\text{ m/s}$
   2. B.$1260\text{ m/s}$
   3. C.$27.4\text{ m/s}$
   4. D.$523\text{ m/s}$
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   Answer: D

5. Q462023 · 10 Apr 2023 · Shift 1

   Match List I with List II : $$\begin{array}{llll}& \text{List I}& & \text{List II}\\ \text{(A)}& \text{3 Translational degrees of freedom}& \text{(I)}& \text{Monoatomic gases}\\ \text{(B)}& \text{3 Translational, 2 rotational degrees of freedom}& \text{(III)}& \text{Rigid diatomic gases}\\ \text{(C)}& \text{3 Translational, 2 rotational and 1 vibrational degrees of freedom}& \text{(IV)}& \text{Nonrigid diatomic gases}\\ \text{(D)}& \text{3 Translational, 3 rotational and more than one vibrational degrees of freedom}& \text{(II)}& \text{Polyatomic gases}\end{array}$$ Choose the correct answer from the options given below:

   1. A.(A)-(I), (B)-(III), (C)-(IV), (D)-(II)
   2. B.(A)-(IV), (B)-(III), (C)-(II), (D)-(I)
   3. C.(A)-(IV), (B)-(II), (C)-(I), (D)-(III)
   4. D.(A)-(I), (B)-(IV), (C)-(III), (D)-(II)
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   Answer: A

6. Q332023 · 6 Apr 2023 · Shift 2

   The temperature of an ideal gas is increased from $200\mathrm{K}$ to $800\mathrm{K}$. If r.m.s. speed of gas at $200\mathrm{K}$ is $v_0$. Then, r.m.s. speed of the gas at $800\mathrm{K}$ will be:

   1. A.$v_0$
   2. B.$2v_0$
   3. C.$4v_0$
   4. D.$\frac{v_0}{4}$
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   Answer: B

7. Q462023 · 29 Jan 2023 · Shift 2

   At 300 K, the rms speed of oxygen molecules is $\sqrt{\frac{\alpha +5}{\alpha }}$ times to that of its average speed in the gas. Then, the value of $\alpha$ will be (used $\pi =\frac{22}{7}$)

   1. A.27
   2. B.28
   3. C.24
   4. D.32
   Show answer

   Answer: B

8. Q332023 · 25 Jan 2023 · Shift 1

   The root mean square velocity of molecules of gas is

   1. A.Proportional to temperature $(T)$
   2. B.Inversely proportional to square root of temperature $\left(\sqrt{\frac{1}{T}}\right)$
   3. C.Proportional to square of temperature $(T^2)$
   4. D.Proportional to square root of temperature $(\sqrt{T})$
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   Answer: D

9. Q452023 · 24 Jan 2023 · Shift 1

   Given below are two statements : Statement I : The temperature of a gas is $-73^{\circ }\mathrm{C}$. When the gas is heated to $527^{\circ }\mathrm{C}$, the root mean square speed of the molecules is doubled. Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules. In the light of the above statements, choose the correct answer from the options given below :

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