JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Heat & Thermodynamics

A monoatomic gas performs a work of

\frac{Q}{4}

where Q is the heat supplied to it. The molar heat capaticy of the gas will be

____

R during this transformation.

Where

R

is the gas constant.

Answer: 2

Solution

From the first law of thermodynamics:

Q = Δ E + W

. Given

W = Q /4

, we have

Δ E = Q - Q /4 = 3 Q /4

. For a monoatomic gas,

Δ E = n C_{V} Δ T = n \frac{3 R}{2} Δ T = \frac{3 Q}{4}

, which gives

n Δ T = \frac{Q}{2 R}

. The molar heat capacity is defined as

C = \frac{Q}{n Δ T} = \frac{Q}{Q / ( 2 R )} = 2 R

JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Integer answer

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