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, $A B$ is isothermal and $B C$ is adiabatic.
$W_{A B}=$ positive (as volume is increasing)
and $W_{B C}=$ negative (as volume is decreasing)
$\left|W_{B C}\right| > \left|W_{A B}\right|$, as area under $P-V$ graph gives the work done.
Hecne, $W_{A B}+W_{B C}=W<0$
From the graph itself, it is clear that $P_{3}>P_{1}$