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

a) Determine the thermal efficiency and the rate at which energy is rejected by heat transfer to the cold reservoir, in MW.

(b) 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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