Obtain simplified expressions for βT and α of an ideal gas.

Question

Obtain simplified expressions for [latex] β_T [/latex] and α of an ideal gas.

Accepted Answer

[latex]\beta _T=-\frac{1}{V} \left\lgroup\frac{∂V }{∂P} \right\rgroup _T [/latex] , but [latex]V=\frac{RT}{P}:\left\lgroup\frac{∂V}{∂P} \right\rgroup_T =-\frac{RT}{P^2}:[/latex]
[latex]\beta _T=\left\lgroup-\frac{1}{V} \right\rgroup .\left\lgroup-\frac{RT}{P^2} \right\rgroup =\frac{1}{P}[/latex]

and [latex]\alpha =\frac{1}{V}\left\lgroup\frac{∂V}{∂T} \right\rgroup _P[/latex] , but [latex]V=\frac{RT}{P}:\left\lgroup\frac{∂V}{∂T} \right\rgroup_P =\frac{R}{P} :[/latex]

[latex]\alpha =\frac{1}{V}.\frac{R}{P} =\frac{1}{T}[/latex]

Question 1.11.2: Obtain simplified expressions for βT and α of an ideal gas.

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