= Excluded-volume ideal gas
{title2=$p(V-b)=RT$}
For one mole, a simple repulsive-volume model uses $p(V-b)=RT$ with $b>0$ and domain $V>b$. The <Maxwell relation> and <first law of thermodynamics> give $(\partial U/\partial V)_T=T(\partial p/\partial T)_V-p=0$, so $U=U(T)$. If its molar <heat capacity at constant volume> $C_V$ is <temperature> independent, it is constant, $U=C_VT+U_*$ and $C_p=C_V+R$. Reversible <adiabatic processes> obey $T(V-b)^{R/C_V}=\mathrm{constant}$ or $p(V-b)^{1+R/C_V}=\mathrm{constant}$. All positive-temperature <isotherms> are strictly decreasing and convex; this single-phase model contains no attractive liquid-gas coexistence mechanism. The parameter $b$ is an effective unavailable molar <volume (thermodynamics)>, not automatically the literal geometric <volume (thermodynamics)> of the <molecules>.
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