JEE Advanced 2018 · Paper 2 · Physics Q17

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PhysicsList match+3 / -1Question 17 of 54

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the $PV$ -diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II.

P-V diagram with P₀, 3P₀ on the P-axis and V₀, 3V₀ on the V-axis. Process II: horizontal arrow at 3P₀ from V₀ to 3V₀. Process III: vertical arrow at 3V₀ down from 3P₀ to P₀. Process IV: a curve from (3V₀, P₀) up to (V₀, 3P₀). Process I: a steeper curve from a point on P = P₀ (between V₀ and 3V₀) up to (V₀, 3P₀).

LIST-I

P
In process I
Q
In process II
R
In process III
S
In process IV

LIST-II

1
Work done by the gas is zero
2
Temperature of the gas remains unchanged
3
No heat is exchanged between the gas and its surroundings
4
Work done by the gas is $6P_0V_0$

P → 4; Q → 3; R → 1; S → 2

P → 1; Q → 3; R → 2; S → 4

P → 3; Q → 4; R → 1; S → 2

P → 3; Q → 4; R → 2; S → 1

Answer and worked solution

Official answer: C

Identify the processes.

II is horizontal at $3P_0$ : isobaric. $W=3P_0(3V_0-V_0)=6P_0V_0$ .
III is vertical at $3V_0$ : isochoric. $W=0$ .
IV runs from $(3V_0,P_0)$ to $(V_0,3P_0)$ : $PV=3P_0V_0$ at both ends, so it is isothermal. The temperature is unchanged.
I is the steeper curve into $(V_0,3P_0)$ : adiabatic. No heat is exchanged.

Match. P (I) → 3; Q (II) → 4; R (III) → 1; S (IV) → 2.

(C)

Topics:Thermodynamic processes Work done by a gas

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JEE Advanced 2018 · Paper 2, Physics question 17