Question

A thermodynamic process is shown in figure. In process $a b, 600 \,J$ of heat is added, and in process bd $200\, J$ of heat is added. The total heat added in process $a c d$ is

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

Answer 1

Answer: (B)

There is no volume change in process $a b$,
so $W=0$ Process $b d$ occurs at constant pressure,
so the work done by the system is
$W=P\left(V_{2}-V_{1}\right)$
$=\left(8 \times 10^{4} Pa \right)\left(5 \times 10^{-3} m ^{3}-2 \times 10^{-3} m ^{3}\right)=240 \,J$
Thus the total work for $a b d$ is $W=240\, J$
and the total heat for $a b d$ is $Q=800 \,J$.
$\therefore \Delta U=Q-W=800 \,J -240 \,J =560 \,J$
Because $\Delta U$ is independent of path, the internal energy change is the same for path $a c d$ as for $a b d$, that is, $560\, J$.
The total work for path $a c d$ is
$W=\left(3 \times 10^{4} Pa \right)\left(5 \times 10^{-3} m ^{3}-2 \times 10^{-3} m ^{3}\right)=90\, J$
$\therefore $ Total heat added in the path $a c d$ is
$Q=\Delta U+W=560 \,J +90 \,J =650 \,J$