Question

One mole of a monatomic ideal gas is taken along two cyclic processes E $\to$ F $\to$ G $\to$ E and E $\to$ F $\to$ H $\to$ 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.

List I		List II
P.	$G\to E$	1.	$160p_0{V}_0$ In 2
Q.	$G\to H$	2	$36P_0{V}_0$
R.	$F\to H$	3.	$24P_0{V}_0$
S.	$F\to G$	4.	$31P_0{V}_0$

• A. P $\to$ 4, Q$\to$3, R $\to$ 2, S $\to$ 1
• B. P $\to$ 4, Q$\to$3, R $\to$ 1, S $\to$ 2
• C. P $\to$ 3, Q$\to$1, R $\to$ 2, S $\to$ 4
• D. P $\to$ 1, Q$\to$3, R $\to$ 2, S $\to$ 4

Answer 1

Answer: (A)

In F $\to$ G work done in isothermal process is
$nRTln\left(\frac{V_f}{V_i}\right)=32p_0{V}_{0}ln\left(\frac{32V_0}{V_0}\right)$
$=32p_0{V}_{0}ln{2}^5=160p_0{v}_{0}ln2$
in G $\to E,\Delta W=p_0\Delta v=p_0(31v_0)=31p_0{v}_0$
in G $\to$ work done is less than $31p_0{v}_{0}i.e.,24p_0{v}_0$
in F $\to$ work done is 36 p${}_0{V}_0$