Question

An ideal gas expands isothermally from a volume $V_1$ to $V_2$and then compressed to original volume $V_1$ adiabatically. Initial pressure is p${}_1$ and final pressure 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, F, 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) plus,
$|W_{BC}|>|W_{AB}|$ as area underp- Vgraph gives the work done.
Hence, W${}_{AB}$ + W${}_{BC}$ = W < 0
From the graph itself, it is clear that p${}_3$ > p${}_v$.
Hence, the correct option is (c).
NOTE At point B, slope of adiabatic (process BC) is greater than the slope of isothermal (process AB).