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

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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4

(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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(3)

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)

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

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

Topic Question Set

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