# Specific Heat affected by Pressure

I know the specific heat depends (slightly) on the conditions present. For example, methane's specific heat is 2.5 at 400 K, but 4.5 at higher temperatures. How might specific heat depend on pressure, though. -- if we are under super low pressure (say 6 mbar rather than earth's typical 1014 mbar), how would specific heat change. I am expecting it to differ along with $PV = nRT$, but not sure.

Also, $\Delta H = mc\Delta T$ -- would I need to plug $\Delta PV/nR$ in for $\Delta T$?

• Note that ‘specific heat’ is ambiguous. Apparently, you are referring to the ‘specific heat capacity at constant pressure’ (symbol: $c_p$). Furthermore, it is not permissible to omit the unit. The given specific heat capacity of methane at constant pressure and a temperature of $T=400\ \mathrm K$ is $c_p=2.5\ \mathrm{kJ\ kg^{-1}\ K^{-1}}$.
– user7951
Apr 24, 2016 at 11:04

$$\left(\frac{\partial H}{\partial P}\right)_T=\left[V-T\left(\frac{\partial V}{\partial T}\right)_P\right]$$ This is equal to zero for an ideal gas.