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 $\Delta T$?