Question

A Carnot heat engine receives 3,200 kJ/s of heat from a high temperature source at 825 °C and rejects heat to a cold temperature sink at 15 °C. Please solve following questions:a.What is the thermal efficiency of this engine?b.What is the power delivered by the engine in watts?c.At what rate is heat rejected to the cold temperature sink?d.What is the entropy change of the sink?

Answer 1

a) 0.7377

b) 2.36*10^6 W

c) 839.344 KW

d) 2.9144 KW / K

Step-by-step explanation:

Given:

- Q_h Heat flow in from hot reservoir = 3200 KW

-Temperature of source T_h = 825 C

- Temperature of sink T_l = 15 C

Find:

a) thermal efficiency of this engine

b) power delivered by the engine

c) rate is heat rejected to the cold temperature sink

d) entropy change of the sink

Solution:

The thermal efficiency n_th of a Carnot heat engine is given by:

n_th = 1 - (T_l / T_h)

n_th = 1 - (15+273 / 825+273)

n_th = 0.7377

The amount of heat rejected can for a carnot engine is given by:

Q_l / Q_h = T_1 / T_h

Q_l = Q_h *(T_1 / T_h)

Q_l = 3200 *(288 / 1098)

Q_l = 839.344 KW

The net power delivered is determined by W_out:

W_out = Q_h - Q_l

W_out = 3200 - 839.344

W_out = 2.36*10^6 W

The change in entropy of sink dS:

dS = Q_l / T_l

dS = 839.344 / 288

dS = 2.914 KW / K