First slide

First law of thermodynamics

Question

P-V curve of a diatomic gas is shown in the figure. Find the total heat given to the gas in the process $A \to B \to C$

Moderate

A

$P_{0} V_{0} + 2 P_{0} V_{0} \ln 2$
B

$\frac{1}{2} P_{0} V_{0} + P_{0} V_{0} \ln 2$
C

$\frac{5}{2} P_{0} V_{0} + 2 P_{0} V_{0} \ln 2$
D

$3 P_{0} V_{0} + 2 P_{0} V_{0} \ln 2$

Solution

From first law of thermodynamics
$∆ Q_{ABC} = ∆ U_{ABC} + ∆ W_{ABC}$
$∆ W_{ABC} = ∆ W_{AB} + ∆ W_{BC} = 0 + {nRT}_{B} \ln \frac{V_{C}}{V_{B}}$
= ${nRT}_{B} \ln \frac{2 V_{0}}{V_{0}}$
= ${nRT}_{B} \ln 2 = 2 P_{0} V_{0} \ln 2$
$∆ U = {nC}_{V} ∆ T = \frac{5}{2} (2 P_{0} V_{0} - P_{0} V_{0})$
$\Rightarrow ∆ Q_{ABC} = \frac{5}{2} P_{0} V_{0} + 2 P_{0} V_{0} \ln 2$

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