Question

In the $P-V$ diagram shown in figure $ABC$ is a semicircle. The work done in the process $A\to B\to C$ is

• A. Zero
• B. $\frac{\pi }{2}atm-L$
• C. $-\frac{\pi }{2}atm-L$
• D. $4atm-L$

Answer 1

Answer: (B)

$\frac{\pi }{2}atm-L$

$Given,ABCisasemicircleofradius1$

$Weknowthat,workdoneisareaundertheP-Vgraph$

$ForA\to B,\Rightarrow \Delta V_{AB}=-ve\Rightarrow \Delta W_{AB}=-ve$

$ForB\to C,\Rightarrow \Delta V_{BC}=+ve\Rightarrow \Delta W_{BC}=+ve$

$Also,$

$\left|W_{AB}\right|<\left|W_{BC}\right|$

$Hence,totalworkdoneispositive.$

$\Delta W_{ABC}=Areaofsemicircle$

$=\frac{1}{2}\pi (1{)}^2$

$=\frac{\pi }{2}atm-L$

$Hence,option\left(B\right)iscorrect.$