Hi. Could anyone clear my doubts? U_2-U_1= C_v(T_2 - T_1) and H_2 - H_1 = C_p (T_2 - T_1): Do these two equations always valid, regardless the process is adiabatic, isobaric ect? At the first place, I thought one works only for isobaric and another for isochloric, because I see C_v and C_p in the equations. I read an example, both the equations are used , even though the process is adiabatic! Especially the second eqn, how can it be applied to a adiabatic process? dQ = d(U + PV) =dH, and dH is not 0 by the second eqn, due to different temp. but for adiabatic, dQ=0! where is my mistake? Another question, how to get W=R_0 x T x ln(P' / P) for a isothermal process? There are so many formula in thermodynamics, I wonder how you guys master this topic? thanks in advance.