An electrical generating plant operates so that the steam driving its turbines i

Question

An electrical generating plant operates so that the steam driving its turbines is at 960o F, cooling towers keep the cold reservoir at a temperature of 111o F. What is the theoretical maximum efficiency (in %)?

If the plant's fuel cost for one year is 61.0 million dollars when using the cooling towers, estimate the yearly saving in fuel cost if the plant used a nearby lake's water to cool the cold reservoir to 52o F while producing the same amount of electricity (in millions of dollars).

I'm not only looking for an answer, however, I'm also looking for reasoning and solution. I want to learn this.
Thanks!

Explanation / Answer

first change all the temperatures in *C by F-32 = 9C/5
=>985*F = 529.44*C = 802.44*K
=>111*F = 43.89*C = 316.89*K
=>52*F = 11.11*C = 284.11*K
By Efficiency(E) = 1 - Tc/Th
=>E1st case = 1 - 316.89/802.44 = 0.6051 = 60.51%
=>E2nd case = 1 - 284.11/802.44 = 0.6459 = 64.59%
Let the amount of energy produced is A thus the fuel requirement with 60.51% efficiency = 100A/60.51 = 1.65A
=>1.65A costs 61 million dollars
=>A = 36.97 million dollars
Let the amount of energy produced is A thus the fuel requirement with 64.59% efficiency = 100A/64.59 = 1.55A = 1.55 x 36.97 = 57.30 million dollars
Thus the yearly saving = 61 - 57.30 = 3.70 yearly saving

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