Using the Maxwell's relations of thermodynamics, obtain the first and second TdS-equations.
Maxwell’s relations are derived from the fundamental thermodynamic potentials and the exactness of their differentials. Starting from the first law of thermodynamics for a closed system, ( dU = TdS - PdV ), where ( U ) is internal energy, ( T ) temperature, ( S ) entropy, ( P ) pressure, and ( V ) volume, we consider ( U ) as a function of natural variables ( S ) and ( V ), i.e., _____ ____ ____ ____ ____.
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Write the expressions of an ideal gas and van der Waals’ equation. 10 moles of nitrogen gas occupy a volume of in a vessel at
. Calculate the pressure exerted by the molecules, if it is assumed to obey van der Waals’ equation. Compare this Value with that obtained using ideal gas law.
Given: ,
and .
Derive an expression of the partition function for a single particle monatomic ideal gas. Write the expression for a monatomic gas consisting of N-identical yet distinguishable and non-interacting particles.
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