Question

$P-V$ diagram of an ideal gas for a process $ABC$ is as shown in the figure. If the total heat absorbed or released by the gas during the process $ABC$ is given by $H=-x{P}_0{V}_0$, what is the value of $x$?

Answer 1

Change in internal energy of the gas during process ABC $\Delta U_{ABC}=0$ (solved earlier)

Process AB : Pressure $P=P_o$ $V_A=3V_o$ $V_B=V_o$

$\therefore$ $W_{AB}=P_o(V_B-V_A)=P_o(V_o-3V_o)=-2P_o{V}_o$

Process BC : $V=V_o=constant$

Thus $$W_{BC} = 0$

$⟹W_{ABC}=W_{AB}+W_{BC}=-2P_o{V}_o+0=-2P_o{V}_o$

From 1st law, $Q_{ABC}+\Delta U_{ABC}+W_{ABC}$

$\therefore$ $Q_{ABC}=0-2P_o{V}_o=-2P_o{V}_o$