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Kinetic Theory — NEET & JEE MCQs with answers
Kinetic theory explains the macroscopic properties of gases — pressure, temperature, specific heat — in terms of the random motion and collisions of molecules. Developed by Maxwell, Boltzmann and others, it successfully predicts gas laws, Avogadro's hypothesis, specific heat capacities of mono/di/polyatomic gases via the equipartition theorem, and the mean free path of molecules.
Topics in this chapter
- 12.1 Introduction
- 12.2 Molecular Nature of Matter
- 12.3 Behaviour of Gases
- 12.4 Kinetic Theory of an Ideal Gas
- 12.5 Law of Equipartition of Energy
- 12.6 Specific Heat Capacity
- 12.7 Mean Free Path
Free practice questions
At constant volume, 2 moles of a diatomic gas with a vibrational mode ($C_v=\frac{7}{2}R$) is heated by $20\,\mathrm{K}$. The heat absorbed is (use $R=8.31\,\mathrm{J\,mol^{-1}\,K^{-1}}$):
- A. $1496\,\mathrm{J}$
- B. $831\,\mathrm{J}$
- C. $1163\,\mathrm{J}$
- D. $748\,\mathrm{J}$
Show answer
Answer: C — $Q=\mu C_v\Delta T=2\times\frac{7}{2}R\times20=140R=140\times8.31=1163.4\approx1163\,\mathrm{J}$.
NCERT Class 11 Physics · Ch 12 · 12.6 Specific Heat Capacity
NCERT uses the average speed of air molecules in estimating the mean free path. This value of $\langle v\rangle$ is taken as:
- A. $340\,\text{m/s}$
- B. $273\,\text{m/s}$
- C. $485\,\text{m/s}$
- D. $1500\,\text{m/s}$
Show answer
Answer: C — NCERT estimate (Eq. 12.41): 'air molecules with average speeds $\langle v\rangle = 485\,\text{m/s}$.'
NCERT Class 11 Physics · Ch 12 · 12.7 Mean Free Path
If the internal energy per mole of a gas at temperature T is (3/2)RT, the gas is:
- A. Rigid diatomic
- B. Monatomic
- C. Polyatomic
- D. Non-rigid diatomic
Show answer
Answer: B — (3/2)RT corresponds to 3 degrees of freedom — purely translational — i.e. a monatomic gas (Section 12.5).
NCERT Class 11 Physics · Ch 12 · 12.5 Law of Equipartition of Energy
An ideal gas sample of $N$ molecules each of mass $m$ at temperature $T$ is in a vessel of volume $V$. Using $E=\frac{3}{2}k_BNT$ and $PV=\frac{2}{3}E$, the pressure is:
- A. $P=\dfrac{3 k_B N T}{2V}$
- B. $P=\dfrac{k_B N T}{V}$
- C. $P=\dfrac{3 k_B N T}{V}$
- D. $P=\dfrac{2 k_B N T}{3V}$
Show answer
Answer: B — $PV=\frac{2}{3}E=\frac{2}{3}\cdot\frac{3}{2}k_BNT=k_BNT$, so $P=k_BNT/V=nk_BT$.
NCERT Class 11 Physics · Ch 12 · 12.4 Kinetic Theory of an Ideal Gas
The perfect gas equation $PV = \mu RT$ requires the temperature $T$ to be expressed in:
- A. degrees Celsius
- B. kelvin (absolute temperature)
- C. any temperature scale
- D. degrees Fahrenheit
Show answer
Answer: B — NCERT: the temperature $T$ is the absolute temperature; choosing the kelvin scale gives $R = 8.314\ \text{J mol}^{-1}\text{K}^{-1}$.
NCERT Class 11 Physics · Ch 12 · 12.3 Behaviour of Gases
According to the NCERT, the atoms are much freer in gases and can
- A. move only along the container walls
- B. remain rigidly fixed in place
- C. never collide at all
- D. travel long distances without colliding
Show answer
Answer: D — The NCERT states that the atoms are much freer in gases and can travel long distances without colliding; if not enclosed, gases disperse away.
NCERT Class 11 Physics · Ch 12 · Molecular Nature of Matter
For which states of matter are the short range inter-atomic forces stated to be important in the NCERT Introduction?
- A. Solids and liquids
- B. Gases only
- C. All states equally
- D. Plasma only
Show answer
Answer: A — The NCERT Introduction states that inter-atomic forces are short range forces that are important for solids and liquids, and can be neglected for gases.
NCERT Class 11 Physics · Ch 12 · Introduction
For a monatomic gas, what is the value of $C_p+C_v$ in terms of $R$?
- A. $R$
- B. $3R$
- C. $\frac{5}{3}R$
- D. $4R$
Show answer
Answer: D — For monatomic gas $C_p=\frac{5}{2}R$, $C_v=\frac{3}{2}R$, so $C_p+C_v=\frac{5}{2}R+\frac{3}{2}R=4R$.
NCERT Class 11 Physics · Ch 12 · 12.6 Specific Heat Capacity
At temperature T, the ratio of the total internal energy of a non-linear polyatomic gas (3 translational + 3 rotational, no vibration) to that of a monatomic gas, for equal moles, is:
- A. 2 : 1
- B. 3 : 2
- C. 1 : 2
- D. 5 : 3
Show answer
Answer: A — Polyatomic = 3RT, monatomic = (3/2)RT. Ratio = 3/(3/2) = 2:1 (Section 12.5).
NCERT Class 11 Physics · Ch 12 · 12.5 Law of Equipartition of Energy
If the number density $n$ of a gas is doubled at constant molecular diameter, the mean free path becomes:
- A. Unchanged
- B. Four times the original
- C. Half of the original
- D. Double the original
Show answer
Answer: C — Since $l \propto 1/n$ (from $l = 1/(\sqrt{2}n\pi d^{2})$), doubling $n$ halves $l$. So the new mean free path is $l/2$.
NCERT Class 11 Physics · Ch 12 · 12.7 Mean Free Path
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