JEE Advanced · 2008 · 13 Apr 2008 · Paper 1 · Heat & Thermodynamics

An ideal gas is expanding such that

P T^{2} =

constant . The coefficient of volume expansion of the gas is

(A) $\frac{1}{T}$
(B) $\frac{2}{T}$
(C) $\frac{3}{T}$ ✓ Correct
(D) $\frac{4}{T}$

Answer: (C)

Solution

The coefficient of volume expansion is

γ = \frac{1}{V} (\frac{d V}{d T})

. For an ideal gas,

P V = n R T

. Given

P T^{2} = k

(constant), we have

P = \frac{k}{T ^{2}}

. Substituting:

\frac{k}{T ^{2}} V = n R T

, so

V = \frac{n R T ^{3}}{k}

. Thus

\frac{d V}{d T} = \frac{3 n R T ^{2}}{k} = \frac{3 V}{T}

, giving

γ = \frac{1}{V} \cdot \frac{3 V}{T} = \frac{3}{T}

JEE Advanced · 2008 · 13 Apr 2008 · Paper 1 · Single correct option

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