n-moles of an ideal gas with constant volume heat capacity $\mathrm{C}_{\mathrm{V}}$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is

(C) $\frac{4 n R}{C_{v}+n R}$

(D) $\frac{4 n R}{\mathrm{C}_{\mathrm{v}}-\mathrm{nR}}$

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Heat & Thermodynamics

n-moles of an ideal gas with constant volume heat capacity

C_{V}

undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is

(A) $\frac{n R}{C _{v} - n R}$
(B) $\frac{n R}{C _{v} + n R}$ ✓ Correct
(C) $\frac{4 n R}{C _{v} + n R}$
(D) $\frac{4 n R}{C _{v} - nR}$

Answer: (B)

Solution

For a constant-pressure process the work is

W = n R Δ T

and the heat is

Q = n C_{P} Δ T

with

C_{P} = C_{V} + R

by Mayer's relation. The fraction of the supplied heat that reappears as work is

\frac{W}{Q} = \frac{n R Δ T}{( C _{V} + n R ) Δ T} = \frac{n R}{C _{V} + n R}

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Single correct option

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