JEE Main · 2017 · 02 Apr 2017 · Offline · Heat & Thermodynamics

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C_{p}

and

C_{v}

are specific heats at constant pressure and constant volume respectively. It is observed that

C_{p} - C_{v} = a

for hydrogen gas

C_{p} - C_{v} = b

for nitrogen gas
The correct relation between a and b is:

(A) $a = 14 b$ ✓ Correct
(B) $a = 28 b$
(C) $a = \frac{1}{14} b$
(D) $a = b$

Answer: (A)

Solution

The subtlety is that these are specific heats, measured per unit mass, not molar. For one gram,

C_{p} - C_{v} = \frac{R}{M}

with

M

the molar mass. So

a = \frac{R}{2}

for hydrogen (

M = 2

) and

b = \frac{R}{28}

for nitrogen (

M = 28

), and dividing,

\frac{a}{b} = \frac{28}{2} = 14

, that is

a = 14 b

. Were these molar heat capacities instead,

C_{p} - C_{v} = R

for both and they would be equal — the per-gram wording is exactly what tips the balance.

JEE Main · 2017 · 02 Apr 2017 · Offline · Single correct option

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