JEE Advanced 2023 · Paper 2 · Physics Q13

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PhysicsInteger+4Question 30 of 51

One mole of an ideal gas undergoes two different cyclic processes I and II, as shown in the $P$ - $V$ diagrams below. In cycle I, processes $a, b, c$ and $d$ are isobaric, isothermal, isobaric and isochoric, respectively. In cycle II, processes $a', b', c'$ and $d'$ are isothermal, isochoric, isobaric and isochoric, respectively. The total work done during cycle I is $W_I$ and that during cycle II is $W_{II}$ . The ratio $W_I/W_{II}$ is _____.

Two P (Pa) against V (m^3) diagrams, both clockwise cycles. (I): a is isobaric at 4P0 from V0 to 2V0; b is an isothermal curve from (2V0, 4P0) down to (4V0, 2P0); c is isobaric at 2P0 back from 4V0 to V0; d is isochoric at V0 from 2P0 up to 4P0. (II): a' is an isothermal curve from (V0, 4P0) to (2V0, 2P0); b' is isochoric at 2V0 down from 2P0 to P0; c' is isobaric at P0 back from 2V0 to V0; d' is isochoric at V0 from P0 up to 4P0.

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Answer and worked solution

Official answer: 2

Write $nRT$ as $PV$ at any point of an isotherm.

Cycle I (clockwise):

Step	Process	Work
a	$4P_0$ , $V_0\to2V_0$	$4P_0V_0$
b	isotherm, $PV=8P_0V_0$ , $2V_0\to4V_0$	$8P_0V_0\ln2$
c	$2P_0$ , $4V_0\to V_0$	$-6P_0V_0$
d	isochoric	0

$W_I=P_0V_0(8\ln2-2)$ .

Cycle II (clockwise):

Step	Process	Work
a′	isotherm, $PV=4P_0V_0$ , $V_0\to2V_0$	$4P_0V_0\ln2$
b′	isochoric	0
c′	$P_0$ , $2V_0\to V_0$	$-P_0V_0$
d′	isochoric	0

$W_{II}=P_0V_0(4\ln2-1)$ .

$\frac{W_I}{W_{II}}=2.$

Topics:Work done by a gas Thermodynamic processes

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JEE Advanced 2023 · Paper 2, Physics question 13