At low pressure, the Berthelot equation is given as: V ˉ = P RT + b − R T 2 a (Where V = molar volume of gas and a , b are constants). What should be the expression for the coefficient of thermal

Question

At low pressure, the Berthelot equation is given as:

$\overset{ˉ}{V}$ $= \frac{RT}{P} + b - \frac{a}{R T ^{2}}$

(Where $V$ = molar volume of gas and $a$ , $b$ are constants).

What should be the expression for the coefficient of thermal expansion, [ $α$ ], at a higher temperature range?

$α = \frac{1}{V ˉ} (\frac{\partial V ˉ}{\partial T})_{P}$

TestHub · Accepted Answer

If T is very large, then V = P RT ​ + b . And ∂ T ∂ V ​ = P R ​ + R T 3 2 a ​ ≃ P R ​ . Therefore, α ≃ [ P RT ​ + b ] 1 ​ × [ P R ​ ] α = T 1 ​ [ 1 + RT P b ​ 1 ​ ] α = T 1 ​ [ 1 + RT P b ​ ] − 1

Chemistry - Real Gas Question with Solution | TestHub

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