Mock Test – JEE Main – Physics- KINETIC THEORY OF GASES

Q1.

The root mean square (rms) speed of a gas molecule is given by:

A) $\sqrt{\frac{3kT}{m}}$m3kT​​
B) $\sqrt{\frac{2kT}{m}}$m2kT​​
C) $\sqrt{\frac{kT}{2m}}$2mkT​​
D) $\sqrt{\frac{kT}{m}}$mkT​​

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Q2.

The pressure of an ideal gas is due to:

A) Intermolecular attraction
B) Collisions of molecules with walls
C) Gravitational force on molecules
D) Vibrations of molecules

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Q3.

The average kinetic energy of a gas molecule is proportional to:

A) Pressure
B) Temperature
C) Volume
D) Mass

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Q4.

For 1 mole of an ideal gas, internal energy depends on:

A) Temperature only
B) Pressure only
C) Volume only
D) Both P and V

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Q5.

A gas contains molecules of mass $m$m and rms speed $v$v. The total kinetic energy of N molecules is:

A) $\frac{1}{2} Nm v^2$21​Nmv2
B) $\frac{3}{2} Nm v^2$23​Nmv2
C) $\frac{1}{2} m v^2$21​mv2
D) $\frac{3}{2} kT$23​kT

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Q6.

Pressure of 1 mole of ideal gas at temperature T and volume V:

A) $\frac{RT}{V}$VRT​
B) $\frac{2RT}{3V}$3V2RT​
C) $\frac{RT}{2V}$2VRT​
D) $\frac{3RT}{2V}$2V3RT​

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Q7.

Most probable speed of molecules in ideal gas:

A) $\sqrt{\frac{2kT}{m}}$m2kT​​
B) $\sqrt{\frac{3kT}{m}}$m3kT​​
C) $\sqrt{\frac{kT}{m}}$mkT​​
D) $\sqrt{\frac{5kT}{m}}$m5kT​​

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Q8.

Degrees of freedom of a diatomic molecule at room temperature:

A) 3
B) 5
C) 6
D) 2

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Q9.

Average translational kinetic energy per molecule is:

A) $\frac{1}{2} kT$21​kT
B) $\frac{3}{2} kT$23​kT
C) $\frac{5}{2} kT$25​kT
D) $3 kT$3kT

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Q10.

A gas molecule has mass $m$m and average kinetic energy $E$E. The rms speed is:

A) $\sqrt{\frac{2E}{m}}$m2E​​
B) $\sqrt{\frac{3E}{m}}$m3E​​
C) $\sqrt{\frac{E}{m}}$mE​​
D) $\sqrt{\frac{E}{2m}}$2mE​​

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Q11.

Internal energy of monoatomic ideal gas per mole:

A) $\frac{3}{2} RT$23​RT
B) $\frac{5}{2} RT$25​RT
C) $\frac{7}{2} RT$27​RT
D) $2 RT$2RT

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Q12.

Ratio of specific heats for monoatomic ideal gas ($\gamma = C_p/C_v$γ=Cp​/Cv​):

A) 5/3
B) 7/5
C) 3/2
D) 4/3

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Q13.

The root mean square speed of oxygen molecule at 27°C is approximately 480 m/s. If temperature doubles, rms speed becomes:

A) 960 m/s
B) 680 m/s
C) 480 m/s
D) 240 m/s

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Q14.

The gas exerts pressure on the wall:

A) Only when molecules move in x-direction
B) Due to collisions in all directions
C) Only when velocity is maximum
D) Only near the wall

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Q15.

If the number of molecules in a container is doubled at same temperature:

A) rms speed doubles
B) Pressure doubles
C) Volume doubles
D) Internal energy halves

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Q16.

Degrees of freedom for nonlinear triatomic molecule:

A) 3
B) 5
C) 6
D) 9

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Q17.

Mean free path is:

A) Distance travelled before collision
B) Average distance between collisions
C) Speed × time
D) Twice the molecular radius

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Q18.

Time between successive collisions of a gas molecule is:

A) Mean free path ÷ rms speed
B) rms speed ÷ mean free path
C) 2 × mean free path ÷ rms speed
D) Half of rms speed × mean free path

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Q19.

Boltzmann constant k relates:

A) Gas constant to Avogadro’s number
B) Pressure and volume
C) Temperature and volume
D) Energy and mass

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Q20.

Fraction of molecules moving with speed between $v$v and $v + dv$v+dv follows:

A) Maxwell-Boltzmann distribution
B) Bernoulli distribution
C) Gaussian distribution
D) Fermi-Dirac distribution

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Q21.

For a monoatomic gas, if temperature is halved:

A) rms speed halves
B) rms speed decreases by √2
C) rms speed decreases by 1/4
D) rms speed remains same

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Q22.

Kinetic theory assumes molecules:

A) Have negligible volume, elastic collisions
B) Attract each other strongly
C) Move in circles
D) Always at rest

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Q23.

If the pressure and volume are doubled, temperature:

A) Doubles
B) Remains same
C) Quadruples
D) Halves

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Q24.

Average translational kinetic energy per mole for a gas:

A) $\frac{3}{2} kT$23​kT
B) $\frac{3}{2} RT$23​RT
C) $\frac{5}{2} RT$25​RT
D) $2 RT$2RT

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Q25.

Internal energy of a diatomic gas at room temperature:

A) $\frac{3}{2} RT$23​RT
B) $\frac{5}{2} RT$25​RT
C) $3 RT$3RT
D) $7/2 RT$7/2RT

Answer

Question No.	Answer
1	A
2	B
3	B
4	A
5	B
6	A
7	A
8	B
9	B
10	A
11	A
12	A
13	B
14	B
15	B
16	D
17	B
18	A
19	A
20	A
21	B
22	A
23	A
24	B
25	B

Solution

KINETIC THEORY OF GASES – DETAILED SOLUTIONS

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Q1. RMS speed of a gas molecule

$$v_\text{rms} = \sqrt{\frac{3kT}{m}}$$vrms​=m3kT​​

This is the standard formula.

Answer: A

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Q2. Source of pressure in an ideal gas

Pressure arises due to collisions of molecules with the walls.

Answer: B

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Q3. Average kinetic energy proportionality

$$E_\text{avg} = \frac{3}{2} kT$$Eavg​=23​kT

Depends only on temperature.

Answer: B

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Q4. Internal energy of 1 mole of ideal gas

Depends only on temperature, not on pressure or volume:$$U = \frac{3}{2} RT \quad \text{(monoatomic)}$$U=23​RT(monoatomic)

Answer: A

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Q5. Total kinetic energy of N molecules

$$E_\text{total} = \frac{1}{2} m v_\text{rms}^2 \times N \quad \text{for each molecule?}$$Etotal​=21​mvrms2​×Nfor each molecule?

Actually, for RMS speed $v_\text{rms}$vrms​:$$E_\text{total} = \frac{1}{2} m N v_\text{rms}^2$$Etotal​=21​mNvrms2​

Answer: B

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Q6. Pressure of 1 mole of ideal gas

$$PV = RT \implies P = \frac{RT}{V}$$PV=RT⟹P=VRT​

Answer: A

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Q7. Most probable speed $v_p$vp​

$$v_p = \sqrt{\frac{2kT}{m}}$$vp​=m2kT​​

Answer: A

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Q8. Degrees of freedom of a diatomic molecule at room temp

• Translational: 3
• Rotational: 2
• Vibrational modes negligible at room temp

$\Rightarrow$⇒ Total $f = 5$f=5

Answer: B

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Q9. Average translational kinetic energy per molecule

$$\langle E_\text{trans} \rangle = \frac{3}{2} kT$$⟨Etrans​⟩=23​kT

Answer: B

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Q10. RMS speed from average kinetic energy

$$E = \frac{1}{2} m v_\text{rms}^2 \implies v_\text{rms} = \sqrt{\frac{2E}{m}}$$E=21​mvrms2​⟹vrms​=m2E​​

Answer: A

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Q11. Internal energy per mole (monoatomic)

$$U = \frac{3}{2} RT$$U=23​RT

Answer: A

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Q12. Ratio of specific heats for monoatomic gas

$$\gamma = \frac{C_p}{C_v} = \frac{5/2 R}{3/2 R} = 5/3$$γ=Cv​Cp​​=3/2R5/2R​=5/3

Answer: A

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Q13. RMS speed at doubled temperature

$$v_\text{rms} \propto \sqrt{T} \implies v_\text{new} = 480 \sqrt{2} \approx 680\,\text{m/s}$$vrms​∝T​⟹vnew​=4802​≈680m/s

Answer: B

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Q14. Pressure on wall due to molecules

• Collisions occur in all directions
• Contribution along x, y, z combined

Answer: B

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Q15. Doubling number of molecules at same T

• RMS speed depends on temperature → unchanged
• Pressure $P = \frac{NkT}{V}$P=VNkT​ → doubles

Answer: B

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Q16. Degrees of freedom of nonlinear triatomic molecule

• Translational: 3
• Rotational: 3
• Vibrational: neglected at room temp

Total $f = 6$f=6

Answer: D

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Q17. Mean free path

• Average distance travelled between successive collisions

Answer: B

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Q18. Time between successive collisions

$$t = \frac{\text{mean free path}}{v_\text{rms}}$$t=vrms​mean free path​

Answer: A

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Q19. Boltzmann constant

$$k = \frac{R}{N_A}$$k=NA​R​

Relates gas constant to Avogadro number

Answer: A

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Q20. Distribution of molecular speeds

• Follows Maxwell-Boltzmann distribution

Answer: A

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Q21. Temperature halved

$$v_\text{rms} \propto \sqrt{T} \implies v_\text{new} = v_\text{old}/\sqrt{2}$$vrms​∝T​⟹vnew​=vold​/2​

Answer: B

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Q22. Assumptions of kinetic theory

• Molecules have negligible volume
• Collisions are elastic

Answer: A

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Q23. Pressure & volume doubled

$$PV = nRT \implies T \text{ doubles}$$PV=nRT⟹T doubles

Answer: A

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Q24. Average translational kinetic energy per mole

$$E_\text{avg} = \frac{3}{2} RT$$Eavg​=23​RT

Answer: B

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Q25. Internal energy of diatomic gas (room temp)

• Translational: 3/2 RT
• Rotational: RT (2 × 1/2 RT)
• Total: 5/2 RT

Answer: B