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Q.

An ideal gas is expending such that $P T^{2} = C$ . If gas expands from 0K, the co-efficient of volume expansion of the gas is $\frac{x}{T}$ . The value of x is _______

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Detailed Solution

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$P T^{2} = C$

$\frac{η R T}{v} . T^{2} = C$

$T^{3} V^{- 1} = C$

Differentiating $\frac{3 T^{2}}{V} \cdot d T - \frac{T^{3}}{V^{2}} d V = 0$

$3 dT = \frac{T}{V} \cdot dV \Rightarrow d V = V (\frac{3}{T}) d T$

Hence, the coefficient of volume expansion

$γ = \frac{d V}{V . d T} = \frac{3}{T}$

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An ideal gas is expending such that PT2=C. If gas expands from 0K, the co-efficient of volume expansion of the gas is xT. The value of x is _______