One mole of mono-atomic 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 1 with the magnitudes of the work done in List 2 and select the correct answer using the codes given below the lists

Open in App

Solution

$A . \to (4)$ ; $B . \to (3)$ ;
$C . \to (2)$ ; $D . \to (1)$

Apply $P V^{1 + 2 / 3} =$ constant for $F$ to $H$ .

$(32 P_{0}) V_{0}^{5 / 3} = P_{0} V_{H}^{5 / 3} \Rightarrow V_{H} = 8 V_{0}$

For path $F G P V =$ constant

$\Rightarrow (32 P_{0}) V_{0} = P_{0} V_{G} \Rightarrow V_{G} = 32 V_{0}$

Work done in $G E = 31 P_{0} V_{0}$

Work done in $G H = 24 P_{0} V_{0}$

Work
done in $F H = \frac{P_{H} V_{H} - P_{F} V_{F}}{(- 2 / f)} = 36 P_{0} V_{0}$
Work done in $F G = R T l n (\frac{V_{G}}{V_{F}})$

$= 160 P_{0} V_{0} ln 2$

Suggest Corrections

Similar questions

E \to F \to G \to E

E \to F \to H \to E

P - V

E \to F \to G \to E

E \to F \to H \to E

P - V

List - I	List - II
P. In process I	1. Work done by the gas is zero
Q. In process II	2. Temperature of the gas remains unchanged
R. In process III	3. No heat is exchanged between the gas and its surroundings
S. In process IV	4. Work done by the gas is $6 P_{0} V_{0}$

P V

List-I	List-II
P. In process I	1. Work done by the gas is zero
Q. In process II	2 Temperature of the gas remains unchanged
R. In process III	3 No heat is exchanged between the gas and its surroundings
S. In process IV	4 Work done by the gas is $6 P_{0} V_{0}$

A B C D A

P - V

Join BYJU'S Learning Program