An ideal gas undergoes a quasi static, 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 $\mathrm{PV}^{\mathrm{n}}=$ constant, then n is given by (Here $\mathrm{C}_{\mathrm{P}}$ and $\mathrm{C}_{\mathrm{V}}$ are molar specific heat at constant pressure and constant volume, respectively):

(A) $n=\frac{C-C_{p}}{C-C_{v}}$

(B) $n=\frac{C_{p}-C}{C-C_{v}}$

(C) $n=\frac{C-C_{v}}{C-C_{p}}$

JEE Main · 2016 · 03 Apr 2016 · Offline · Heat & Thermodynamics

An ideal gas undergoes a quasi static, 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

PV^{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) $n = \frac{C - C _{p}}{C - C _{v}}$ ✓ Correct
(B) $n = \frac{C _{p} - C}{C - C _{v}}$
(C) $n = \frac{C - C _{v}}{C - C _{p}}$
(D) $n = \frac{C _{p}}{C _{v}}$

Answer: (A)

Solution

For a polytropic process

P V^{n}

= constant the molar heat capacity is

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

. All the heat capacity above

C_{V}

therefore comes from that single term, so

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

, which means

1 - n = \frac{R}{C - C _{V}}

. Rearranging,

n = 1 - \frac{R}{C - C _{V}} = \frac{C - C _{V} - R}{C - C _{V}}

. Now use Mayer's relation

R = C_{P} - C_{V}

, so the numerator becomes

C - C_{V} - (C_{P} - C_{V}) = C - C_{P}

. Hence

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

JEE Main · 2016 · 03 Apr 2016 · Offline · Single correct option

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JEE Main · 2016 · 03 Apr 2016 · Offline · Heat & Thermodynamics

Solution

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