Question

3. A newly built engine operates between the

room temperature (21 oC) and the melting point of

silver (961 oC) and claims to have an actual

efficiency of 75.0 %.

a) How much mechanical energy per cycle does

the engine deliver if it absorbs 3.50 x 106 J of heat

everycycle (from the hot bath) assuming this claim

is true?

b) How much thermal energy does the engine

reject per cycle to the colder reservoir at 21o C

if the claim is true?

c) What is the maximum thermal efficiency of

an ideal Carnot cycle operating between the same

two reservoirs? Do you think that the engine's

claim is justified based on this? Explain.

d) What is the change in entropy of the universe that actual engine produces per cycle (assuming that

the claim of 72% efficiency is true)? Do you think

that the engine's claim is justified based on this?

Explain

Answer 1

Assuming the claim to be 75% eta = work done/Heat absorbed work done = eta times Heat absorbed = 0.75 times 3.5 times 10^6 = 2.625 times 10^6 J Heat Absorbed = work done + Heat rejected Therefore Heat rejected = 3.5 times 10^6 - 2.625 times 10^6 = 0.875 times 10^6 J eta_max = Carnot efficiency = 1 - T_L/T_H = 1 - (273 + 21/273 + 961) = 1 - 294/1234 = 76.175 5 As the efficiency is greater than the claim of 75% the claim is justified Delta S_H = Delta Q_H/T_H = -3.5 times 10^6/273 + 361 = -2.8363 kJ/kelvin Negative sign indicates heat rejection Delta S_c = Delta Q_c/T_c = 0.875 times 10^6/273 + 21 = + 2.9761 kJ/kelvin Delta S-uni = Delta S_H + Delta S_c = 2.9761 - 2.8363 = 0.1398 kJ/kelvin The engine claim is again justified as the Delta S_uni is positive