Question

The graph below represents the pressure and volume for a gas undergoing a cyclic process (X to Y to Z to X). Assume that Y and Z are on the same horizontal line, and Z and X are on the same vertical line. The area inside the shape $X-Y-Z-X$ is $1000J$.
If the heat absorbed by the gas during process $X-Y$ is $2000J$ and the heat released by the gas during process $Y-Z$ is $3000J$, how much heat is lost or gained during process $Z-X$?

• A. $2000J$ is gained
• B. $2000J$ is lost
• C. $1000J$ is gained
• D. $1000J$ is lost
• E. $5000J$ is gained

Answer 1

The correct option is A $2000J$ is gained

Let the transfer of heat during the process $Z-X$ be $x$.

Total heat transferred in the cyclic process $Q=2000-3000+x=x-1000$ J

Work done by the gas $W=1000$ J

In a cyclic process, $\Delta U=0$ J

From 1st law of thermodynamics : $Q=\Delta U+W$

$\therefore$ $x-1000=0+1000$ $⟹x=+2000$ J

Hence heat is gained during process $Z-X$.