A) \[{{C}_{V}}={{\left( \frac{\delta u}{\delta T} \right)}_{p}}\]
B) \[{{\left( \frac{\delta H}{\delta T} \right)}_{V}}\]
C) \[{{C}_{p}}-{{C}_{V}}=R\] for one mole of an ideal gas
D) \[{{\left( \frac{\delta u}{\delta V} \right)}_{T}}=-\frac{a}{{{V}^{2}}}\](internal pressure in van der Waals' equation)
Correct Answer: C
Solution :
The difference of molar heat capacities of a gas at constant pressure\[({{C}_{p}})\]and at constant volume\[({{C}_{V}})\]is equal to the gas constant, R. \[\therefore \]\[{{C}_{p}}-{{C}_{V}}=R\]for one mole of an ideal gas.
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