1)

One mole of a monoatomic ideal gas is taken along two cyclic  processes E→ F→ G→ E  and

E→F→ H→ E as shown in the p-V diagram.

The processes involved are purely isochoric, isobaric, isothermal or adiabatic.

Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists.

A) P:4,Q:3,R:2,S:1

B) P:4,Q:3, R:1, S:2

C) P:3, Q:1, R:2, S:4

D) P:1,Q:3,R:2, S:4

Option A

### Explanation:

in F→ G work done in isothermal process is

$nRT ln\left(\frac{V_{f}}{V_{i}}\right)=32p_{0}V_{0}ln\left(\frac{32V_{0}}{V_{0}}\right)$

$=32p_{0}V_{0}ln2^{5}=160p_{0}V_{0}ln 2$

$In G\rightarrow E, \triangle W=p_{0}\triangle V=p_{0}(31V_{0})=31p_{0}V_{0}$

In G $\rightarrow$ H , work done is less than 31 p0V0 , i.e, 24 p0V0

In F $\rightarrow$ H workdone is 36 p0V0