A power cycle operates between hot and cold reservoirs at 600 K and 300 K, respe

Question

A power cycle operates between hot and cold reservoirs at 600 K and 300 K, respectively. At steady state the cycle develops a power output of 0.45 MW while receiving energy by heat transfer from the hot reservoir at the rate of 1 MW. Determine the thermal efficiency and the rate at which energy is rejected by heat transfer to the cold reservoir, in MW. Compare the results of part (a) with those of a reversible power cycle operating between these reservoirs and receiving the same rate of heat transfer from the hot reservoir.

Explanation / Answer

a)T1= 600 K
T2 = 300 K
W_output = .45 MW
Q_1 = 1MW
now heat rejected to the cold reservoir = Q_2 = Q_1 - W = 1 - 0.45 MW = 0.55MW (by first law)
also efficiency = W_output / Q1 = 0.45/1 = 0.45

= 45 %
b) for a reversible cycle efficiency is given by , = 1- T2/T1
= 1 - 300/600 =0.5
= 50 %
also W_output/ Q1 = 0.5 ()
W_output = 0.5 x 1 =0.5 MW
and rate at which the heat is rejected =Q2 = Q1 - W_output = 1 - 0.5 = 0.5 MW

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