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Any help with this problem is appreciated and will be ratedlifesaver. Thanks
Problem: According to Kerry Emanuel, a professor of atmospheric sciences at MIT, "The mature hurricane is an almost perfect example of a Carnot heat engine.1" The figure below illustrates the 4 steps of a hurricane Carnot cycle; the figure caption provides the description from Emanuel. According to Emmanuel, at point A, air undergoes an isothermal expansion as it flows towards the lower pressure of the storm center crossing the sea surface at TH=300 K. When the air reaches a critical distance from the storms center (about 15-20 km) the air turns abruptly upward. The ascent is adiabatic and reversible. At C, heat is radiated isothermally to space at Tc=200 K. To complete the cycle, air undergoes a reversible adiabatic compression from D to A. Although we will only use the term "air" to describe the fluid within the hurricane, a real hurricane is composed of a mixture of air plus water vapor and suspended condensed water (next quarter we'll talk about mixtures of air and water vapor). On a T-s diagram, sketch the 4-step process indicating steps A through D and the appropriate temperatures. W is the thermodynamic efficiency of a Carnot cycle operating between these two temperatures? The Carnot cycle model can be used to estimate the hurricane wind speeds (V is the hurricane wind speeds). The rate of net work or power of the hurricane is associated with the winds; this power is then converted back to heat through frictional dissipation. An estimate of the power per unit area of the ocean surface is given by D = CDrhoV3 where CD is a constant (drag coefficient) and rho is the air density. The total rate of heat input per unit area is given by Q = CkrhoVE + CDrhoV3 where Ck is another constant (enthalphy exchange coefficient) and E is the evaporative potential of the sea surface (units of E are kJ/kg). Using these terms, find an equation t relates the wind speed V to the temperatures TH and TC and some of the parameters given above. Assume t the ratio of Ck to CD is one. If E= 12 kJ/kg, estimate the wind speed.

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