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## Homework Statement

The equation of state of an ideal gas is p = nkT, where p is the thermodynamic

pressure and n = N / V is the thermodynamic variable for the number of particles per

unit volume. The n dependence of the free energy f per unit volume of the ideal gas is

obtained by the following expression , where c is temperature-dependent constant k is boltzmann constant.

(a) nkT[In(n)+c]

(b) 2nkT[n ln(n)+c.]

(c) 3/2 nkT

(d) 3nkT

## Homework Equations

∂f/∂n=μ

pV=NkT

p=NkT/V

## The Attempt at a Solution

internal energy U=U(S,V,N)

∴μ=∂U/∂N

and ∂μ/∂V=∂

^{2}U/∂N∂V= -∂p/∂N

∂μ/∂V=-kT/V

∴μ=-kTlnV+c