JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Heat & Thermodynamics

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Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be:

(A)525 J✓ Correct
(B)441 J
(C)572 J
(D)735 J

Answer: (A)

Solution

A diatomic gas whose molecules rotate but do not oscillate has five degrees of freedom, giving

C_{V} = \frac{5}{2} R

and

C_{P} = \frac{7}{2} R

. At constant pressure the heat supplied is

Q = n C_{P} Δ T

while the rise in internal energy is

Δ U = n C_{V} Δ T

, so their ratio is

\frac{Δ U}{Q} = \frac{C _{V}}{C _{P}} = \frac{5}{7}

whatever the amount of gas. With

Q = 735 J

, the internal energy rises by

\frac{5}{7} \times 735 = 525 J

JEE Main · 2023 · 31 Jan 2023 · Shift 2 · Single correct option

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