A heat engine receives 1000kJ/s of heat from a high temperature source at 600◦C and rejects heat to a cold temperature sink at 20◦C 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?

Answer:

(A)  the thermal efficiency of this engine is 66.44 %

(B)  the power delivered by the engine in watts is 664,400 W

(C) The rate at which heat is rejected to the cold temperature sink is 335.6 kJ/s.

Explanation:

Given;

Input Heat received by the engine, [tex]P_{in}[/tex] = 1000 kJ/s

hot temperature, [tex]T_H[/tex] = 600 ⁰C = 600 + 273 = 873 K

cold temperature, [tex]T_C[/tex] = 20 ⁰C = 20 + 273 = 293 K

(A)  the thermal efficiency of this engine;

[tex]\eta = 1 - \frac{T_C}{T_H} \\\\\eta = 1 - \frac{293}{873} \\\\\eta = 1 - 0.3356\\\\\eta = 0.6644 = 66.44 \%[/tex]

(B) the power delivered by the engine in watts;

[tex]P = \eta P_{in}\\\\P = 0.6644 \times \ 1000kJ/s \ \times \ \frac{1\ kW}{1\ kJ/s} \\\\P = 664.4 \ kW \\\\P = 664,400 \ W[/tex]

(C)  The rate at which heat is rejected to the cold temperature sink;

[tex]Q_C = Q_H(1-\eta)\\\\Q_C = 1000\ kJ/s(1-0.6644)\\\\Q_C = 335.6 \ kJ/s[/tex]

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