# conservation of total_enthalpy and total_energy

 Following conclusions based on thermodynamic definitions could be useful when checking for conservation of total_energy or total_enthalpy in a system.Definitions:Enthalpy = h = Internal_Energy + Pressure * Volume = U + PV........... (1)Total_Energy = E = Internal_Energy + Kinetic_Energy + Potential_Energy = U + 0.5(u^2) + PE........ (2)Total_Entahlpy = H = Enthalpy + 0.5*(u^2) = h + 0.5(u^2)................. (3)Work done: Constant Volume: 1W2= 0 Constant Pressure: 1W2= Pressure * Volume_Change = P(V2-V1)........ (4)E = H - PV [from (1), (3), (2), neglecting PE]........ (5)First Law of Thermodynamics: Heat_Change = Work_done + Energy_change===> 1Q2 = 1W2 + E2 - E1For a constant volume process(W=0) and adiabatic process (Q=0):E2 - E1 = 0 ; change in total_energy is conserved.===> From (5):(H2-H1) - (PV2 - PV1)=0So, for a constant volume and adiabatic process, change in total_energy is zero.For constant pressure process: 1Q2 = P(V2- V1) + (U2- U1) + 0.5(u2^2 - u1^2) [from (5), (2),(4) and neglecting PE] 0 = H2 - H1 [from (3), adibatic process 1Q2=0]So, for a constant pressure and adiabatic process, change in total_enthalpy is zero.