Question

A thermodynamic process is shown in figure. In process $ab,600J$ of heat is added, and in process bd $200J$ of heat is added. The total heat added in process $acd$ is

• A. 550 J
• B. 650 J
• C. 750 J
• D. 850 J

Answer 1

Answer: (B)

There is no volume change in process $ab$,
so $W=0$ Process $bd$ occurs at constant pressure,
so the work done by the system is
$W=P\left(V_2-V_1\right)$
$=\left(8\times 10^{4}Pa\right)\left(5\times 10^{-3}{m}^3-2\times 10^{-3}{m}^3\right)=240J$
Thus the total work for $abd$ is $W=240J$
and the total heat for $abd$ is $Q=800J$.
$\therefore \Delta U=Q-W=800J-240J=560J$
Because $\Delta U$ is independent of path, the internal energy change is the same for path $acd$ as for $abd$, that is, $560J$.
The total work for path $acd$ is
$W=\left(3\times 10^{4}Pa\right)\left(5\times 10^{-3}{m}^3-2\times 10^{-3}{m}^3\right)=90J$
$\therefore$ Total heat added in the path $acd$ is
$Q=\Delta U+W=560J+90J=650J$