Question

A cycle followed by an engine ( made of one mole of an ideal gas in a cylinder with a piston) is shown in figure. The heat exchanged by the engine with the surroundings at constant volume is (Take $C_V$ = $\frac{3}{2}$ R)

• A. $(P_B-P_A)V_A$
• B. $\frac{1}{2}(P_B-P_A)V_A$
• C. $\frac{3}{2}(P_B-P_A)V_A$
• D. $\frac{5}{2}(P_B-P_A)V_A$

Answer 1

The correct option is C $\frac{3}{2}(P_B-P_A)V_A$

For any process

$dQ=dV+dW$

$\because$ known $AB$ is isochoric

So, $dw=0$

$dQ=dV$

$dQ=CvdT$

$Q=\int dQ={\int }_A^{B}CvdT$

$=Cv.[T{]}_A^B=Cv(T_B-T_A)$

$=Cv[\frac{P_B{V}_B}{R}-\frac{P_A{V}_A}{R}]$

$=\frac{3}{2}R\left[\frac{P_B{V}_B-P_A{V}_A}{R}\right][\because V_A=V_B]$

$=\frac{3}{2}[P_B-P_A]V_A$