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Thermodynamic process

An ideal gas undergoes a quasistatic, reversible process in wh

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An ideal gas undergoes a quasistatic, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $p$ and volume $V$ is given by $p V^{n} =$ constant, then $n$ is given by (Here $C_{p}$ and $C_{V}$ are molar specific heat at constant pressure and constant volume, respectively)
(a) $n = \frac{C _{p}}{C _{V}}$
(b) $n = \frac{C - C _{p}}{C - C _{V}}$
(c) $n = \frac{C _{p} - C}{C - C _{V}}$
(d) $n = \frac{C - C _{V}}{C - C _{p}}$

Views: 5,681 students

Updated on: Apr 8, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2019

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Lucas Discussed

An ideal gas undergoes a quasistatic, reversible process in which its molar heat capacity

C

remains constant. If during this process the relation of pressure

p

and volume

V

is given by

p V^{n} =

constant, then

n

is given by (Here

C_{p}

and

C_{V}

are molar specific heat at constant pressure and constant volume, respectively)
(a)

n = \frac{C _{p}}{C _{V}}

(b)

n = \frac{C - C _{p}}{C - C _{V}}

(c)

n = \frac{C _{p} - C}{C - C _{V}}

(d)

n = \frac{C - C _{V}}{C - C _{p}}

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

Exp. (b)
For polytropic process, specific heat for an ideal gas,

C = \frac{R}{1 - n} + C_{V}

∴ \frac{R}{1 - n} + C_{V} = C

\Rightarrow \frac{R}{1 - n} = C - C_{V}

\Rightarrow \frac{R}{C - C _{V}} = 1 - n (where, R = C_{p} - C_{V})

\Rightarrow \frac{C _{p} - C _{V}}{C - C _{V}} = 1 - n

\Rightarrow n = 1 - \frac{C _{p} - C _{V}}{C - C _{V}} \Rightarrow n = \frac{C - C _{p}}{C - C _{V}}

Thus, number of moles

n

is given by

n = \frac{C - C _{p}}{C - C _{V}}

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Question Text	An ideal gas undergoes a quasistatic, reversible process in which its molar heat capacity $C$ remains constant. If during this process the relation of pressure $p$ and volume $V$ is given by $p V^{n} =$ constant, then $n$ is given by (Here $C_{p}$ and $C_{V}$ are molar specific heat at constant pressure and constant volume, respectively) (a) $n = \frac{C _{p}}{C _{V}}$ (b) $n = \frac{C - C _{p}}{C - C _{V}}$ (c) $n = \frac{C _{p} - C}{C - C _{V}}$ (d) $n = \frac{C - C _{V}}{C - C _{p}}$
Updated On	Apr 8, 2023
Topic	Thermodynamics
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 5
Upvotes	684
Avg. Video Duration	7 min

Text solutionVerified

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