Top Kinetic Theory PYQs for NEET Preparation

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Topic Question Set

Q 1 :
The value of $γ = (\frac{C_{p}}{C_{v}})$ , for hydrogen, helium and another ideal diatomic gas $X$ (whose molecules are not rigid but have an additional vibrational mode), are respectively equal to [2019]

$\frac{7}{5}, \frac{5}{3}, \frac{9}{7}$
$\frac{5}{3}, \frac{7}{5}, \frac{9}{7}$
$\frac{5}{3}, \frac{7}{5}, \frac{7}{5}$
$\frac{7}{5}, \frac{5}{3}, \frac{7}{5}$

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3

4

(1)

$γ = 1 + \frac{2}{n}$ ; For $H_{2},$ $γ = 1 + \frac{2}{5} = \frac{7}{5}$

For He, $γ = 1 + \frac{2}{3} = \frac{5}{3}$ ; For $X,$ $γ = 1 + \frac{2}{7} = \frac{9}{7}$

Q 2 :
A gas mixture consists of 2 moles of $O_{2}$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is [2017]

15 RT
9 RT
11 RT
4 RT

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(3)

The internal energy of 2 moles of $O_{2}$ atom is

$U_{O_{2}} = \frac{n_{1} f_{1}}{2} R T = 2 \times \frac{5}{2} R T = 5 R T$

The internal energy of 4 moles of Ar atom is

$U_{A r} = \frac{n_{2} f_{2} R T}{2} = 4 \times \frac{3}{2} R T = 6 R T$

$∴$ The total internal energy of the system is

$U = U_{O_{2}} + U_{A r} = 5 R T + 6 R T = 11 R T$

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