A Carnot engine operates between 300 K and 600 K. If the entropy change during heat addition is 1 kJ/K, the work produced by the engine is:

Concept:

Entropy change for heat addition is given by \(dS = \frac{{dQ}}{T}\)

\({\eta _{carnot}} = 1 - \frac{{{T_L}}}{{{T_H}}}\)

\(\eta = \frac{{Power\;Input}}{{Heat\;Input}}\)

Calculation:

Given:

dS = 1 kJ/K

Therefore heat addition,

\(1 = \frac{{dQ}}{{600\;K}}\)

dQ = 600 kJ

Now,

\({\eta _{carnot}} = 1 - \frac{{300}}{{600}} = 0.5\)

\(0.5 = \frac{{Power\;output}}{{600}}\)

∴ Power output = 300 kJ