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

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]

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Topic Question Set

Q 2 : Energy of 10 non rigid diatomic molecules at temperature T is [2024] .question-row { display: flex; align-items: flex-start; gap: 8px; } .q-no { font-size: 17px; white-space: nowrap; margin-left: -15px; } .q-text { font-size: 18px; flex: 1; } .q-no, .q-text p { line-height: 30px; }

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Q 2 :

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