Question

An ideal gas expands isothermally from a volume $V_1$ and $V_2$ and then compressed to original volume adiabatically. Initial pressure is $P_1$ and final ressure is $P_3$ The total work done is $W$. Then:

• A. $P_3>P_1,W>0$
• B. $P_3<P_1,W<0$
• C. $P_3>P_1,W<0$
• D. $P_3=P_1,W=0$

Answer 1

Answer: (C)

Slope of adiabatic process at a given state $(P,V,T)$ is more than the slope of isothermal process. The corresponding $P-V$ graph for the two processes is as shown in figure.

In the graph, $AB$ is isothermal and $BC$ is adiabatic.
$W_{AB}=$ positive (as volume is increasing)
and $W_{BC}=$ negative (as volume is decreasing)
$\left|W_{BC}\right|>\left|W_{AB}\right|$, as area under $P-V$ graph gives the work done.
Hecne, $W_{AB}+W_{BC}=W<0$
From the graph itself, it is clear that $P_3>P_1$