Page 246 - Standard Handbook Of Petroleum & Natural Gas Engineering

Thermodynamics 219

(2-137)

Combining the first law Equation 2-102 with the second law equation 2-1 11 yields
the expression
dU = TdS - 6W = d(TS) - 6W

or
6W = -d(U - TS)
which, upon integration between states 1 and 2, yields

W = -A(U - TS) (reversible isothermal processes) (2-1 38)
The combination of properties U - TS occurs so frequently in thermodynamic
analysis that it is given a special name and symbol, namely A, the workfunction or
maximum work (because it represents the maximum work per unit mass, obtainable
during any isothermal reversible change in any given system). Therefore, it is seen that
W,,,.$, = -AA (reversible isothermal process) (2-139)
Note that the maximum work depends only upon the initial and final states of a
system and not upon the path.
Maximum Useful Work: Free Energy

The first and second law expressions can be combined and written for constant
temperature, constant pressure processes:
dU = TdS - 6W = TdS - PdV - 6W' (2-140)
where FW' represents all work energy exchanged with the surroundings except
P-V work that is written as PdV. Therefore, solving for FW gives
-6W' = dU + PdV - TdS (2-141)

or, because both ?' and P are constant,
-6W' = dU + d( PV) - d(TS)

or
-6W' = -d(U + PV - TS) (2-142)
By integration this becomes

W' = -A(U + PV - TS)
= -A(H - TS) (constant temperature and pressure) (2-143)