Kinetic Theory of Gases and ldeal Gas | Physics JEE previous year questions with Solutions

Q 1 :

The translational degrees of freedom $(f_{t})$ and rotational degrees of freedom $(f_{r})$ of $C H_{4}$ molecule are [2024]

$f_{t} = 3$ and $f_{r} = 3$
$f_{t} = 2$ and $f_{r} = 3$
$f_{t} = 2$ and $f_{r} = 2$
$f_{t} = 3$ and $f_{r} = 2$

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(1)

$C H_{4}$ is polyatomic and non-linear,

The degrees of freedom of $C H_{4}$ are

Translational degrees of freedom $f_{t} = 3$
Rotational degrees of freedom $f_{r} = 3$

Q 2 :

Energy of 10 non rigid diatomic molecules at temperature T is [2024]

$35$ $K_{B}$ $T$
$35$ $R T$
$\frac{7}{2}$ $R T$
$70$ $K_{B}$ $T$

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(1)

Degree of freedom of non-rigid diatomic

$M o l e c u l e s \to f \to R o t a t i o n + T r a n s l a t i o n + V i b r a t i o n$

$↓$ $↓$ $↓$

$2$ $3$ $2$

Degree of freedom, $f = 2 + 3 + 2 = 7$

Energy of one molecule = $\frac{f}{2} K_{B} T$

energy of 10 molecules

$= 10 (\frac{f}{2} K_{B} T) = 10 (\frac{7}{2} K_{B} T) = 35 K_{B} T$

Q 3 :

The average kinetic energy of a monoatomic molecule is 0.414eV at temperature

(Use $K_{B} = 1.38 \times 10^{- 23} J / m o l - K$ ) [2024]

3000 K
3200 K
1600 K
1500 K

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(2)

For monoatomic molecule degree of freedom = 3.

$∴$ $K = \frac{3}{2} K_{B} T$

$T = \frac{0.414 \times 1.6 \times 10^{- 19} \times 2}{3 \times 1.38 \times 10^{- 23}} = 3200 K$

Q 4 :

The total kinetic energy of 1 mole oxygen at 27°C is :

[Use universal gas constant (R) = 8.31J/ mole K] [2024]

6845.5 J
5942.0 J
6232.5 J
5670.5 J

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(3)

Kinetic energy = $\frac{f}{2} n R$

$= \frac{5}{2} \times 1 \times 8.31 \times 300 J = 6232.5 J$

Q 5 :

N moles of a polyatomic gas (f = 6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is [2024]

4
3
6
2

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(1)

$f_{e q} = \frac{n_{1} f_{1} + n_{2} f_{2}}{n_{1} + n_{2}}$

For diatomic gas $f_{e q} = 5$

$5 = \frac{(N) (6) + (2) (3)}{N + 2}$

$5 N + 10 = 6 N + 6 \Rightarrow N = 4$

Q 6 :

The parameter that remains the same for molecules of all gases at a given temperature is [2024]

kinetic energy
mass
speed
Momentum

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(1)

$K E = \frac{f}{2} k T$

Conceptual

Q 7 :

The kinetic energy of translation of the molecules in 50 g of ${CO}_{2}$ gas at 17°C is: [2025]

3986.3 J
4102.8 J
4205.5 J
3582.7 J

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(2)

Kinetic energy of translation $= \frac{3}{2} n RT$

$n = \frac{50 g}{44 g} = \frac{25}{22} mol$

T = 17°C = 290 K

Kinetic energy of translation

${(KE)}_{Translational} = \frac{3}{2} (\frac{25}{22}) (8.3) (290) J = 4102.8 J$

Q 8 :

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is:

(Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol) [2025]

1 : 10
10 : 1
$1 : \sqrt{10}$
1 : 1

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(4)

K.E = $\frac{f}{2}$ kT

For He and Ar, $f = 3$

$\frac{{KE}_{He}}{{KE}_{Ar}} = \frac{1}{1}$

Q 9 :

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is [2023]

$\frac{3}{2} R$
$\frac{7}{2} R$
$\frac{9}{2} R$
$\frac{5}{2} R$

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(2)

Diatomic gas molecules have three translational degrees of freedom, two rotational degrees of freedom, and it is given that it has one vibrational mode. So there are two additional degrees of freedom corresponding to one vibrational mode. Therefore, total degrees of freedom = 7

$C_{V} = \frac{f R}{2} = \frac{7 R}{2}$

Q 10 :

A flask contains hydrogen and oxygen in the ratio of 2 : 1 by mass at temperature 27°C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is [2023]

2 : 1
1 : 1
1 : 4
4 : 1

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(2)

$K_{av} = \frac{5}{2} k T$

Ratio = 1 : 1

Q 11 :

The number of air molecules per ${cm}^{3}$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$ . The ratio of collision frequency of air molecules before and after the increase in number respectively is [2023]

0.75
0.50
0.25
1.25

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(3)

$Collision frequency,$

$f = \frac{V}{λ} = \frac{V}{(\frac{1}{\sqrt{2} π d^{2} n_{v}})} = \sqrt{2} π d^{2} v n_{v}$

$∴$ $f \propto n, n_{v} is number density$

$\frac{f_{1}}{f_{2}} = \frac{n_{v_{1}}}{n_{v_{2}}} = \frac{3 \times 10^{19}}{12 \times 10^{19}} = 0.25$

Q 12 :

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27°C is [2023]

627°C
327°C
927°C
1227°C

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(2)

$Kinetic energy = \frac{f}{2} k T, where T is the absolute temperature.$

$If K_{1} is the kinetic energy at 27 ° C$

$and K_{2} is the kinetic energy at new temperature T .$

$\frac{K_{1}}{K_{2}} = \frac{T_{1}}{T_{2}} \Rightarrow \frac{1}{2} = \frac{300}{T}$

$T = 600 K \Rightarrow T = 327 ° C$

Q 13 :

Match List I with List II: [2023]

List I List II

A. 3 Translational degrees of freedom I. Monoatomic gases

B. 3 Translational, 2 rotational degrees of freedoms II. Polyatomic gases

C. 3 Translational, 2 rotational and 1 vibrational degrees of freedom III. Rigid diatomic gases

D. 3 Translational, 3 rotational and more than one vibrational degrees of freedom IV. Non rigid diatomic gases

Choose the correct answer from the options given below:

(A) – (IV), (B) – (III), (C) – (II), (D) – (I)
(A) – (IV), (B) – (II), (C) – (I), (D) – (III)
(A) – (I), (B) – (III), (C) – (IV), (D) – (II)
(A) – (I), (B) – (IV), (C) – (III), (D) – (II)

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Factual

Type of gases	No. of degrees of freedom
Monoatomic gas	3T
Diatomic + rigid	3T + 2R
Diatomic + non-rigid	3T + 2R + 1V
Polyatomic gas	3T + 3R + more than 1V

T = Translational degree of freedom

R = Rotational degree of freedom

V = Vibrational degree of freedom

Q 14 :

A flask contains Hydrogen and Argon in the ratio 2 : 1 by mass. The temperature of the mixture is 30°C. The ratio of average kinetic energy per molecule of the two gases $(K_{argon} / K_{hydrogen})$ is: (Given: Atomic weight of Ar = 39.9) [2023]

1
2
$\frac{39.9}{2}$
39.9

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(1)

$Average kinetic energy per molecule = \frac{3}{2} k T$

$\frac{K_{Ar}}{K_{H}} = \frac{1}{1}$

Q 15 :

Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is $32 \times 10^{8} s^{- 1}$ then collision frequency in gas A is____________/s [2026]

$32 \times 10^{8}$
$8 \times 10^{8}$
$2 \times 10^{8}$
$4 \times 10^{8}$

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(4)

$Collision frequency (Z) = \sqrt{2} π d^{2} N \sqrt{\frac{8 R T}{π M}}$

Temp, N are same

$Z \propto \frac{d^{2}}{\sqrt{M}}$

$d_{A} = \frac{d_{B}}{2}$

$M_{A} = 4 M_{B}$

$\frac{Z_{A}}{Z_{B}} = \frac{d_{A}^{2}}{\sqrt{M_{A}}} \times \frac{\sqrt{M_{B}}}{d_{B}^{2}} = (\sqrt{\frac{M_{B}}{M_{A}}}) {(\frac{d_{A}}{d_{B}})}^{2}$

$= (\sqrt{\frac{1}{4}}) {(\frac{1}{2})}^{2}$

$\frac{Z_{A}}{Z_{B}} = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$

$\Rightarrow Z_{A} = \frac{32 \times 10^{8}}{8} = 4 \times 10^{8} s^{- 1}$

Topic Question Set

Q 1 :

The translational degrees of freedom $(f_{t})$ and rotational degrees of freedom $(f_{r})$ of $C H_{4}$ molecule are [2024]

Q 2 :

Energy of 10 non rigid diatomic molecules at temperature T is [2024]

Q 3 :

The average kinetic energy of a monoatomic molecule is 0.414eV at temperature

(Use $K_{B} = 1.38 \times 10^{- 23} J / m o l - K$ ) [2024]

Q 4 :

The total kinetic energy of 1 mole oxygen at 27°C is :

[Use universal gas constant (R) = 8.31J/ mole K] [2024]

Q 5 :

N moles of a polyatomic gas (f = 6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is [2024]

Q 6 :

The parameter that remains the same for molecules of all gases at a given temperature is [2024]

Q 7 :

The kinetic energy of translation of the molecules in 50 g of ${CO}_{2}$ gas at 17°C is: [2025]

Q 8 :

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is:

(Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol) [2025]

Q 9 :

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is [2023]

Q 10 :

A flask contains hydrogen and oxygen in the ratio of 2 : 1 by mass at temperature 27°C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is [2023]

Q 11 :

The number of air molecules per ${cm}^{3}$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$ . The ratio of collision frequency of air molecules before and after the increase in number respectively is [2023]

Q 12 :

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27°C is [2023]

Q 14 :

A flask contains Hydrogen and Argon in the ratio 2 : 1 by mass. The temperature of the mixture is 30°C. The ratio of average kinetic energy per molecule of the two gases $(K_{argon} / K_{hydrogen})$ is: (Given: Atomic weight of Ar = 39.9) [2023]

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	List I		List II
A.	3 Translational degrees of freedom	I.	Monoatomic gases
B.	3 Translational, 2 rotational degrees of freedoms	II.	Polyatomic gases
C.	3 Translational, 2 rotational and 1 vibrational degrees of freedom	III.	Rigid diatomic gases
D.	3 Translational, 3 rotational and more than one vibrational degrees of freedom	IV.	Non rigid diatomic gases

Topic Question Set

Q 1 : The translational degrees of freedom (ft) and rotational degrees of freedom (fr) of CH4 molecule are [2024]

Q 2 : Energy of 10 non rigid diatomic molecules at temperature T is [2024]

Q 3 : The average kinetic energy of a monoatomic molecule is 0.414eV at temperature (Use KB=1.38×10-23J/mol-K) [2024]

Q 4 : The total kinetic energy of 1 mole oxygen at 27°C is : [Use universal gas constant (R) = 8.31J/ mole K] [2024]

Q 5 : N moles of a polyatomic gas (f = 6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is [2024]

Q 6 : The parameter that remains the same for molecules of all gases at a given temperature is [2024]

Q 7 : The kinetic energy of translation of the molecules in 50 g of CO2 gas at 17°C is: [2025]

Q 8 : The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is: (Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol) [2025]

Q 9 : According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is [2023]

Q 10 : A flask contains hydrogen and oxygen in the ratio of 2 : 1 by mass at temperature 27°C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is [2023]

Q 11 : The number of air molecules per cm3 increased from 3×1019 to 12×1019. The ratio of collision frequency of air molecules before and after the increase in number respectively is [2023]

Q 12 : The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27°C is [2023]

Q 14 : A flask contains Hydrogen and Argon in the ratio 2 : 1 by mass. The temperature of the mixture is 30°C. The ratio of average kinetic energy per molecule of the two gases (Kargon/Khydrogen) is: (Given: Atomic weight of Ar = 39.9) [2023]

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Q 1 :

The translational degrees of freedom $(f_{t})$ and rotational degrees of freedom $(f_{r})$ of $C H_{4}$ molecule are [2024]

Q 2 :

Energy of 10 non rigid diatomic molecules at temperature T is [2024]

Q 3 :

The average kinetic energy of a monoatomic molecule is 0.414eV at temperature

(Use $K_{B} = 1.38 \times 10^{- 23} J / m o l - K$ ) [2024]

Q 4 :

The total kinetic energy of 1 mole oxygen at 27°C is :

[Use universal gas constant (R) = 8.31J/ mole K] [2024]

Q 5 :

N moles of a polyatomic gas (f = 6) must be mixed with two moles of a monoatomic gas so that the mixture behaves as a diatomic gas. The value of N is [2024]

Q 6 :

The parameter that remains the same for molecules of all gases at a given temperature is [2024]

Q 7 :

The kinetic energy of translation of the molecules in 50 g of ${CO}_{2}$ gas at 17°C is: [2025]

Q 8 :

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is:

(Give: Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/mol) [2025]

Q 9 :

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is [2023]

Q 10 :

A flask contains hydrogen and oxygen in the ratio of 2 : 1 by mass at temperature 27°C. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is [2023]

Q 11 :

The number of air molecules per ${cm}^{3}$ increased from $3 \times 10^{19}$ to $12 \times 10^{19}$ . The ratio of collision frequency of air molecules before and after the increase in number respectively is [2023]

Q 12 :

The temperature at which the kinetic energy of oxygen molecules becomes double than its value at 27°C is [2023]

Q 14 :

A flask contains Hydrogen and Argon in the ratio 2 : 1 by mass. The temperature of the mixture is 30°C. The ratio of average kinetic energy per molecule of the two gases $(K_{argon} / K_{hydrogen})$ is: (Given: Atomic weight of Ar = 39.9) [2023]