An ideal gas is expanding such that PT2=constant. The coefficient of volume expansion of the gas is [2008]

Question

An ideal gas is expanding such that $P T^{2} = constant .$ The coefficient of volume expansion of the gas is [2008]

Smart Achievers · Accepted Answer

(3)

$p T^{2} = constant$ $(given)$

$∴$ $(\frac{n R T}{V}) T^{2} = constant$ or $T^{3} V^{- 1} = constant$

$(∴ P V = n R T)$

Differentiating the equation, we get

$\frac{3 T^{2}}{V} d T - \frac{T^{3}}{V^{2}} d V = 0$ or $3 d T = \frac{T}{V} d V \dots (i)$

From the equation

$d V = V γ d T$

$γ = coefficient of volume expansion of gas = \frac{d V}{V \cdot d T}$

From eq. (i) $γ = \frac{d V}{V \cdot d T} = \frac{3}{T}$

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