= Adiabat with linear heat capacity
{title2=$c_p(T)=A+BT$}
For a fixed-composition <ideal gas>, the reversible <adiabatic process> relation $c_p\,dT/T=R\,dp/p$ gives $A\ln(T/T_s)+B(T-T_s)=R\ln(p/p_s)$. Under <hydrostatic equilibrium>, $gz=A(T_s-T)+B(T_s^2-T^2)/2$. Increasing positive $B$ at fixed surface conditions increases temperature at a given smaller pressure and raises the model's formal zero-temperature height. That finite-height mathematical boundary is not a physical absolute-zero prediction.
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