Basic Chemical Thermodynamics - Elements of Environmental Engineering: Thermodynamics and Kinetics - page 21

C

16

T cold = 200 K

D

T hot = 300 K

A

B

0 100

200

Distance from hurricane center/km

FIGURE 2.3 The hurricane heat engine.

B movement corresponds to a significant decrease in pressure. But, since the sea surface
is an infinite heat reservoir, its temperature is constant. Unlimited heat is therefore added
to the air parcel as it moves from A to B. This amounts to the increased humidity in the
air as the seawater evaporates into the incoming air. At point B the air turns and moves
upward, making the hurricane eye wall. Here the latent heat is converted into sensible
heat as water vapor condenses and pressure decreases rapidly. This is an example of
an adiabatic expansion of air. At point C (12-18 km from the surface), the adiabatic
expansion decreases the air temperature to 200 K.As the air remains at this temperature,
itsinkstopointDtowardthetropopause,whichisnearisothermalconditions.Finally,the
air from point D returns to pointA in a near-adiabatic compression. The thermodynamic
cycle is thus complete and a perfect steam engine is created, except that the energy
produced by the hurricane shows up as the energy of the wind. Thus, we can apply
Carnot's theorem to obtain the maximum wind for an idealized hurricane.
The kinetic energy dissipated by the atmosphere near the surface is given by

D ≈ C D ρ V 2 , (2.18)

where D is the rate of heat energy dissipation per unit surface area, ρ is the air density,
V is the wind speed, and C D is the drag coefficient (recall fluid mechanics).
The total mechanical work done by a Carnot engine is given by
W = Q T hot − T cold
T hot

,

(2.19)

where Q is the heat input rate. The total heat input rate per unit surface area is given by

Q = C K ρ VE 2 + C D ρ V 2 , (2.20)

continued