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Question

One mole of a monoatomic gas is expanded isothermally from state A to state B. Then it is compressed isobarically from B to C and finally the gas returns to intial state A following isochoric process CA. Then heat rejected in the process BC is

Moderate

A

$\frac{4}{3} P_{0} V_{0}$
B

$\frac{5}{2} P_{0} V_{0}$
C

$\frac{3}{2} P_{0} V_{0}$
D

$2 P_{0} V_{0}$

Solution

Since AB is isothermal process, temperature of gas at state point B, $T_{B} = T_{A}$
Now $\frac{2 P_{0} . V_{0}}{T_{A}} = \frac{P_{0} V_{0}}{T_{C}} \Rightarrow T_{C} = T_{A} / 2$
$∴$ Heat rejected $= n . C_{P} . Δ T$
$= 1. (\frac{3 + 2}{2}) R . (T_{B} - T_{C})$
$= \frac{5}{2} R (\frac{T_{A}}{2}) = \frac{5}{4} (R T_{A})$
$= \frac{5}{4} (2 P_{0} V_{0}) = \frac{5}{2} P_{0} V_{0}$

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