JEE Main · 2020 · 06 Sep 2020 · Shift 1 · Heat & Thermodynamics

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Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T.
The total internal energy,

U

of a mole of this gas, and the value of

γ (= \frac{C _{P}}{C _{v}})

are given, respectively, by:

(A) $U = \frac{5}{2} RT$ and $γ = \frac{6}{5}$
(B) $U = 5 RT$ and $γ = \frac{7}{5}$
(C) $U = \frac{5}{2} RT$ and $γ = \frac{7}{5}$ ✓ Correct
(D) $U = 5 RT$ and $γ = \frac{6}{5}$

Answer: (C)

Solution

With three translational and two rotational degrees of freedom the gas has

f = 5

active degrees of freedom. By equipartition the internal energy of one mole is

U = \frac{f}{2} R T = \frac{5}{2} R T

. The ratio of specific heats follows from

γ = 1 + \frac{2}{f} = 1 + \frac{2}{5} = \frac{7}{5}

. So the mole has internal energy

\frac{5}{2} R T

and

γ = \frac{7}{5}

JEE Main · 2020 · 06 Sep 2020 · Shift 1 · Single correct option

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JEE Main · 2020 · 06 Sep 2020 · Shift 1 · Heat & Thermodynamics

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