= Classical ideal gas in a homogeneous soft trap
{title2=$Z_1=VI_n(kT)^{3/2+3/(2n)}$}
For the potential $U=r^{2n}/V^{2n/3}$, rescaling $r=V^{1/3}(kT)^{1/(2n)}u$ in the classical one-particle <partition function> gives the formula above. The parameter-conjugate force is $P=NkT/V$, the <internal energy> is $(3/2+3/(2n))NkT$, and $C_P-C_V=Nk$. The kinetic term contributes $3NkT/2$, while the potential term contributes $3NkT/(2n)$. For indistinguishable particles the $N!$ <factor> changes <free energy> and <entropy> but not these force and heat-capacity formulas.
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