Q.

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.

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a

P → 4;   Q → 3;   R → 1;   S → 2

b

P → 1;   Q → 3;   R → 2;   S → 4

c

P → 3;   Q → 4;   R → 1;   S → 2

d

P → 3;   Q → 4;   R → 2;   S → 1

answer is C.

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Detailed Solution

Process-I is an adiabatic processΔQ=ΔU+W      ΔQ=0            W=−ΔU     Volume of gas is decreasing    ⇒W<0   ΔU>0Temperature of gas increases No heat is exchanged between the gas and surrounding.Process –II is an isobaric process (pressure remain constant)W=PΔV=3P03V0−V0=6P0V0 Process-III is an isochoric process ( volume remain constant) ΔQ=ΔU+W         ⇒ΔQ=ΔU  Process-IV is an isothermal process (temperature remains constant)ΔQ=ΔU+W ⇒ΔU=0
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