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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.
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)
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 - E1
For 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)=0
So, 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.