This problem is about the thermodynamics fundamentals of global circulation and natural convection..

This problem is about the thermodynamics fundamentals of
global circulation and natural convection in general. We explore the
fundamentals in two parts, in accordance with Fig. P9.5.

(a) Consider a stream of ideal gas with the flow rate
m_ which flows isothermally and reversibly through the system shown in
Fig. P9.5a. The temperature T is constant throughout the system. The inlet and
outlet pressures are Pin and Pout. Invoke the first and
second laws, the ideal gas model, and the isothermal and reversible model and
show that the heat input rate __ and work output rate __ are equal
and
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This problem is about the thermodynamics fundamentals of
global circulation and natural convection in general. We explore the
fundamentals in two parts, in accordance with Fig. P9.5.

(a) Consider a stream of ideal gas with the flow rate
__ which flows isothermally and reversibly through the system shown in
Fig. P9.5a. The temperature T is constant throughout the system. The inlet and
outlet pressures are Pin and Pout. Invoke the first and
second laws, the ideal gas model, and the isothermal and reversible model and
show that the heat input rate Q_ and work output rate __ are equal
and given by

(b) Next, the circulation of the atmosphere can be modeled
as a heat engine that functions in a cycle of four processes (Fig. P9.5b): 1–2,
isothermal heating and expansion at TH; 2–3, isobaric cooling at PL;
3–4, isothermal cooling and compression at TL; and 4–1, isobaric
heating at PH. The cycle is executed reversibly: There are no
pressure drops from 2 to 3 and from 4 to 1, and locally, there is no
temperature difference between the 2–3 and 4–1 streams. The internal
(regenerative) heat transfer __ i occurs across a zero
temperature difference. The heating and expansion process is a model for how
the air warms up and rises to higher altitudes (lower pressures) over

the equatorial zone (TH). The cooling and
compression represent a model for the sinking of the same airstream over the
polar zones (TL). The counterflow formed by the 4–1 and 2–3 streams
is a model for the circulation of the atmosphere in the meridional direction.

Use the results of part (a) to calculate the net power
output of the atmospheric heat engine (__ net = __ H
_ WL) and the energy conversion efficiency __ = __ net___
H. Does your resulting expression for __
look familiar? Why?

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