JEE Advanced 2022 Paper 1 · Physics · Thermodynamics and Kinetic Theory of Gases · hard

One mole of a monatomic ideal gas (Cv=3/2R) undergoes the processes in List-I. Match each with its molar heat capacity in List-II. List-I: (P)…

Single correct option

One mole of a monatomic ideal gas (

C_v=\tfrac32R

) undergoes the processes in List-I. Match each with its molar heat capacity in List-II.

List-I: (P)

PV^2=\text{constant}

; (Q)

P\propto V

; (R) constant pressure; (S)

PV^{3/2}=\text{constant}

.

List-II (in units of

R

): (1)

-1/2

; (2)

1/2

; (3)

3/2

; (4)

2

; (5)

5/2

Show answer and solution

Answer: (D) P→2, Q→4, R→5, S→1

For

PV^n=\text{constant}

C=C_v+\dfrac{R}{1-n}

. (P)

n=2

\tfrac32R-R=\tfrac12R

(2). (Q)

P\propto V

means

n=-1

\tfrac32R+\tfrac12R=2R

(4). (R) isobaric (

n=0

\tfrac52R

(5). (S)

n=\tfrac32

\tfrac32R-2R=-\tfrac12R

(1). So P→2, Q→4, R→5, S→1; List-II entry (3)

3/2

(isochoric) is unused.

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