1. The problem statement, all variables and given/known data I know that for constant volume ∂q=du and so du=Cv.dT However i dont understand how did we get to ∂q=du by neglecting the vdP term of enthalpy What im trying to say is, is enthalpy this ∆U+P∂V+V∂P or this ∆U+P∂V? I dont understand since the definition of enthalpy is derived out of a constant pressure volume change And why snt specific heat at constant volume Cv=∆U+V∂P/dT instead of Cv=∆U/dT? Thank you in advance for your answers 2. Relevant equations 3. The attempt at a solution From what I see: ∂Qnet,in=∆U+∂Wnet,out ∂Qnet,in=∆U+P∂V+V∂P C=∂Qnet,in/dT For constant pressure: Cp=∆U+P∂V/dT assuming ∆U+P∂V is enthalpy then ∆H=Cp.∆P For constant volume: Cv=∆U+V∂P/dT but all the books say it actually is just ∆U/dT where did the VdP term go? if we add heat to a fixed volume won't its pressure increase and so VdP would be relevant?