A Carnot engine whose high-temperature reservoir is at 630 K takes in 520 J of h

Question

A Carnot engine whose high-temperature reservoir is at 630 K takes in 520 J of heat at this temperature in each cycle and gives up 320 J to the low-temperature reservoir.

Please show your steps to solve each part.

Part A) How much mechanical work does the engine perform during each cycle? Express your answer in joules to three significant figures.

Part B) What is the temperature of the low-temperature reservoir? Express your answer in kelvins to three significant figures.

Part C) What is the thermal efficiency of the cycle? Express your answer in percent to three significant figures.

Explanation / Answer

Th = 630 K

Heat input, Qi = 520 J

Heat output, Qo = 320 J

a. let mechanical work done by the engine be W

then from conservation of energy

W + Qo = Qi

W = Qi - Qo = 200 J

b. let the temperature of the cold reservoir be Tc

then

for heat capacity c of the workign gas and mass m

mc*630 = Qi = 520

mc*Tc = Qo = 320

Tc = 320*630/520 = 387.6923 K

c. thermal efficiency of the cycle = n

n = W/Qi = 200/520 = 0.3846

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