JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Heat & Thermodynamics

A diatomic gas, having

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

and

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

, is heated at constant pressure. The ratio dU : dQ : dW :

(A) $5 : 7 : 3$
(B) $5 : 7 : 2$ ✓ Correct
(C) $3 : 5 : 2$
(D) $3 : 7 : 2$

Answer: (B)

Solution

Heating at constant pressure gives

d U = n C_{V} d T = \frac{5}{2} n R d T

and

d Q = n C_{P} d T = \frac{7}{2} n R d T

.

The first law then fixes the work:

d W = d Q - d U = (\frac{7}{2} - \frac{5}{2}) n R d T = n R d T

Dividing all three by

n R d T

, the quantities stand in the ratio

\frac{5}{2} : \frac{7}{2} : 1 = 5 : 7 : 2

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option

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