Page 247 - Standard Handbook Of Petroleum & Natural Gas Engineering

220 General Engineering and Science

This expression shows that the maximum possible useful work (Le., reversible work)
that can be obtained from any process occurring at constant temperature and pressure
is a function of the initial and final states only and is independent of the path. The
combination of properties U + PV - TS or H - TS occurs so frequently in thermodynamic
analysis that it is given a special name and symbol, F, thefree energy (sometimes called the
Gibbs Free Energy). Using this definition, Equation 2-143 is written

W',,, = -AF (2-144)
Because F is a function of temperature and pressure, its differential can be written as

dF = ( $)TdP + [E) P dT (2-145)

Since F = U + PV - TS, we can also write
dF = dU + PdV + VdP - TdS - SdT (2-146)
Using Equation 2-130, this becomes

dF = VdP - SdT (2-1 47)
Comparison with Equation 2-145 shows that
($IT = (2-148)

( = -s (2-149)

Example 2-24

An inventor claims to have devised a CO, compressor that requires no shaft
work. The device operates at steady state by transferring heat from a feed stream
of 2 1bJs of CO, at 150 psia and 100°F. The CO, is compressed to a final pressure of
500 psia and a temperature of 40°F. Kinetic and potential energy effects are negligible.
A cold source at -140°F "drives" the device at a heat transfer rate of 60 Btu/sec.
Check the validity of the inventor's claim.
Solution

The device will be impossible if it violates either the first or second law of
thermodynamics. From Figure 2-34 the inlet and outlet properties are:

State 1 State 2
T, = 100°F T, = 40°F
P, = 150 psia P, = 500 psia
h, = 315 BtU/lbm h, = 285 BtU/lbm
S, = 1.31 8 Btu/lb,"R S, = 1.21 5 Btu/lb,"R