The pressure (P) and temperature ( T) relationship of an ideal gas obeys the equation PT² = constant. The volume expansion coefficient of the gas will be: (a) 3T² (b) 3T² (c) 3T³ (d) 3/T

Answer: (d). From PV = nRT: P ∝ T/V. PT² = const ⇒ T/VT² = const ⇒ V ∝ T³. Volume expansion coefficient γV = 1/VdV/dT = 3/T. So the answer is (d) 3/T.

The pressure (P) and temperature ( T) relationship of an ideal gas… | JEE Main 2023 (30 Jan, Shift 1)

Q47JEE Main 2023 · 30 JAN · SHIFT 1Medium

Gas Laws & Ideal Gas Equation

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:

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Answer: (d)

From $PV = nRT$ : $P \propto \frac{T}{V}$ .
$PT^2 =$ const $\Rightarrow \frac{T}{V}T^2 =$ const $\Rightarrow V \propto T^3$ .
Volume expansion coefficient $\gamma_V = \frac{1}{V}\frac{dV}{dT} = \frac{3}{T}$ .
So the answer is (d) $\frac{3}{T}$ .

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