Question 1.2: An ideal gas is characterised by the relation pV = NRT where...

Principles of Thermodynamics [EXP-7769]

An ideal gas is characterised by the relation pV = NRT where p is the pressure of the gas, V is the volume, T is the temperature, N is the number of moles of gas and R is a constant.

a) Calculate the differential dp (T, V).

b) Calculate $\frac{\partial }{\partial T} \Bigl(\frac{\partial p(T,V)}{\partial V }\Bigr)$ and $\frac{\partial }{\partial V} \Bigl(\frac{\partial p(T,V)}{\partial T}\Bigr)$ .

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The differential and partial derivatives of the pressure p (T, V) of an ideal gas are given by,

a) $d p (T, V) = \frac{N R}{V} d T – \frac{N R T}{V^2} d V$ .

b) $\frac{\partial }{\partial T} \Bigl(\frac{\partial p(T,V)}{\partial V }\Bigr)= \frac{\partial }{\partial V} \Bigl(\frac{\partial p(T,V)}{\partial T}\Bigr) =- \frac{N R }{V^2}$ .

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