One of the most efficient engines built so far has the following characteristics: combustion chamber temperature = 1900°C, exhaust temperature = 430°C, 7.0 * 109 cal of fuel produces 1.4 * 1010 J of work in one hour. (a) What is the actual efficiency of this engine? (b) What is the Carnot efficiency of the engine? (c) What is the power output, in hp, of this engine?

actual efficiency is 47.78 %

Carnot efficiency is 67.65 %

power output is 5.20 * 10^3 hp

Explanation:

given data

temperature = 1900°C = 1900 + 273 K = 2173 K

exhaust temperature = 430°C = 430 + 273 K = 703 K

fuel = 7.0 * 10^9 cal

work = 1.4 * 10^10 J

to find out

actual efficiency and Carnot efficiency and power output of engine

solution

first we find actual efficiency that is = work / heat input

put the value and

input energy = 7.0 * 10^9 cal (4.184 J/1 cal) = 29.29 * 10^9 J

actual efficiency = 1.4 * 10^10 / (29.29 * 10^9)

actual efficiency = 0.4778

actual efficiency is 47.78 %

and

Carnot efficiency is = 1 - (703 / 2173)

so Carnot efficiency is = 0.67648

Carnot efficiency is 67.65 %

and

power output = work / time

power output = 1.4 * 10^10 / 3600 sec

power output = 3.88 * 10^6 W

power output = 3.88 * 10^6 W / 746 hp

so power output is 5.20 * 10^3 hp