First slide

Different type of processes

Question

An ideal monoatomic gas undergoes a cyclic process ABCA as shown in the figure. The ratio of heat absorbed during AB to the work done on the gas during BC is

Moderate

A

$\frac{5}{2 \ln 2}$
B

$\frac{5}{3}$
C

$\frac{5}{4 \ln 2}$
D

$\frac{5}{6}$

Solution

AB is a constant pressure process
$Q = {nC}_{p} dT = \frac{nfR}{2} (T_{o})$
BC is constant temperature process
$W = nR 2 T_{o} \ln (\frac{2 V_{o}}{V})$
$= nR 2 T_{o} \ln (2)$
$\frac{Q}{W} = \frac{\frac{nfR}{2} T_{o}}{nR 2 T_{o} \ln (2)} = \frac{5}{4 \ln 2}$

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