In thermodynamics, (delta internal energy) = (delta) U = q + w But it is also known that (delta U) = q_v = integral of (C_v) dT So if C_v is constant, then we have (delta U) = q_v = C_v (delta T) But the confusing part for me is what follows. For instance, in an adiabatic process, for (delta) U = q + w, it is known that q = 0. So (delta) U = w But then again, people will often use (delta U) = q_v = C_v (delta T) for adiabatic processes. This is confusing to me, Isn't q_v esentially the same as q? Except q_v is q at constant volume. So shouldn't q_v = 0 when q = 0?