JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Heat & Thermodynamics

1 mole of rigid diatomic gas performs a work of

\frac{Q}{5}

when heat

Q

is supplied to it. The molar heat capacity of the gas during this transformation is

\frac{x R}{8}

. The value of

x

is ____ [

R =

universal gas constant]

Answer: 25

Solution

The first law gives

Q = Δ U + W

, and with

W = \frac{Q}{5}

the internal energy change is

Δ U = \frac{4 Q}{5}

. For one mole, write both in terms of the same temperature rise:

Q = C Δ T

with

C

the molar heat capacity of this process, and

Δ U = C_{V} Δ T

. Then

C_{V} Δ T = \frac{4}{5} C Δ T \Rightarrow C = \frac{5}{4} C_{V}

A rigid diatomic gas has

C_{V} = \frac{5 R}{2}

, so

C = \frac{5}{4} \times \frac{5 R}{2} = \frac{25 R}{8}

and

x = 25

JEE Main · 2021 · 26 Feb 2021 · Shift 2 · Integer answer

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