Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 22

where C K is the enthalpy exchange coefficient and E is the evaporative potential of the
sea surface. E is a measure of the air-sea thermodynamic equilibrium and is related to
the greenhouse effect (see Chapter 6, Section 6.3.3.2). The larger the greenhouse effect
of gases emitted to the atmosphere, the greater the E value. We now have

+ C D ρ V 2 ) T hot − T cold
T hot

.

W = (C K ρ VE 2

(2.21)

Equating W to D and using algebraic manipulations, we have the final equation for the
hurricane's maximum wind velocity (Emanuel, 2003):

T hot − T cold
T cold

V max = · E . (2.22)

Note that T cold and not T hot appears in the denominator of the above equation. This is
a result of the feedback mechanisms of dissipative heating. The evaporative potential
of the sea surface is approximated by the following equation:

C K

C D · (h ∗ − h) ,

E ≈ (2.23)

where h ∗ and h are, respectively, the specific enthalpy (enthalpy per unit mass) of air
near the ocean boundary surface and of the inflowing dry air in the ambient boundary
layer. The ratio C K : C D has been observed to be about 1 (Emanuel, 2005). The stu-
dent is encouraged to work out Problem 2.33 to learn about the applicability of the
above equations.

2.2.5 E NTHALPY AND H EAT C APACITY
For most chemical processes that are carried out at constant volume, the PV work is
zero since d V is zero. However, there are a number of processes, especially environ-
mentally relevant ones, for which the pressure is constant but the volume is not. In
such cases, the work term is nonzero. It is appropriate for such processes to define
a new term called enthalpy , denoted by the symbol H . It is also a state function that
does not depend on the path taken by a system to arrive at that state. If only expansion
work is considered against a constant external pressure P in Equation 2.2, then we
have the relation

Δ U = q − P Δ V . If the two states of the system are denoted by A

and B, then we have

(U B +

−

(U A +

=

PV B ) PV A ) q . (2.24)

If we define H q at constant P . The importance

of H in dealing with systems involving material flow will become apparent later as
we combine several of the thermodynamic laws. We have seen thus far that the total
energy of the system at constant volume is given by

= U + PV , then we see that Δ H =

Δ U = (q) V , and the total energy

at constant pressure is given by Δ H = (q) P .