Thermodynamic Property Relations for Single Phase Systems
Apart from internal energy and enthalpy, two other ones that are particularly useful in depiction of thermodynamic equilibrium are Helmholtz free energy (A) and Gibbs free energy (G). We defer expanding upon the concept of these two types of energies to chapter 6; however, we state their definition at this point as they are instrumental in the development of property correlations for real fluids.
• Specific Helmholtz free energy: A = U − TS ...(5.1)
• Specific Gibbs free energy: G = H − TS ...(5.2)
For a reversible process in a closed system the first law gives:
dU = dQ + dW
dU = TdS − PdV . ...(5.3)
Using H = U + PV and taking a total differential of both sides:
dH = dU + PdV+ VdP ...(5.4)
Putting eqn. 5.3 in 5.4 we get:
dH = TdS + VdP ...(5.5)
In the same manner as above one may easily show that the following two relations obtain:
dA = −SdT − PdV ...(5.6)
dG = VdP − SdT ...(5.7)
Equations 5.3 to 5.7 comprise the fundamental energy relations for thermodynamic systems where there is a single phase with constant composition. In principle, they may be integrated to compute the energy changes for a system transiting from one equilibrium state to another.