The pressure $(\mathrm{P})$ and temperature $(\mathrm{T})$ relationship of an ideal gas obeys the equation $\mathrm{PT}^{2}=$ constant. The volume expansion coefficient of the gas will be:

(B) $\frac{3}{\mathrm{~T}^{2}}$

(C) $\frac{3}{\mathrm{~T}^{3}}$

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Heat & Thermodynamics

The pressure

(P)

and temperature

(T)

relationship of an ideal gas obeys the equation

PT^{2} =

constant. The volume expansion coefficient of the gas will be:

(A) $3 T^{2}$
(B) $\frac{3}{T ^{2}}$
(C) $\frac{3}{T ^{3}}$
(D) $\frac{3}{T}$ ✓ Correct

Answer: (D)

Solution

From

P V = n R T

P = \frac{n R T}{V}

; putting this into

P T^{2} = constant

gives

\frac{T ^{3}}{V} = constant

, i.e.

V = c T^{3}

. Then

\frac{d V}{d T} = 3 c T^{2}

, so the volume expansion coefficient is

γ = \frac{1}{V} \frac{d V}{d T} = \frac{3 c T ^{2}}{c T ^{3}} = \frac{3}{T}

JEE Main · 2023 · 30 Jan 2023 · Shift 1 · Single correct option

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