JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Heat & Thermodynamics

A sample of gas at temperature

T

is adiabatically expanded to double its volume. The work done by the gas in the process is (given,

γ = \frac{3}{2}

(A) $W = T R [2 - 2]$
(B) $W = \frac{T}{R} [2 - 2]$
(C) $W = \frac{R}{T} [2 - 2]$
(D) $W = R T [2 - 2]$ ✓ Correct

Answer: (D)

Solution

For an adiabatic change

T V^{γ - 1}

is constant, and with

γ = \frac{3}{2}

the exponent is

γ - 1 = \frac{1}{2}

. Doubling the volume,

T V^{1/2} = T_{2} (2 V)^{1/2}

, gives

T_{2} = \frac{T}{2}

. For one mole the work done by the gas is

W = \frac{R ( T _{1} - T _{2} )}{γ - 1} = \frac{R ( T - \frac{T}{2} )}{1/2} = 2 R T (1 - \frac{1}{2}) = R T (2 - 2) .

JEE Main · 2023 · 01 Feb 2023 · Shift 1 · Single correct option

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