Question

A heat engine receives an amount of energy Qh= 790 kJ by heat transfer from a high temperature thermal reservoir at Th=950 K. Energy is rejected by heat transfer to a lower temperature thermal reservoir at T1=590 K. If waste heat in the amount of Q1=160 kJ is rejected to the low temperature thermal reservoir during each cycle.

a) Solve for the maximum theoretical efficiency that an engine in this situation could operate with. ANSWER: 0.379

b) Solve for actual efficiency that the engine is operating with.

c) Which of the following best describes the manner in which the cycle is operating...

-Reversibly or Impossibly?

Answer 1

Temperature of the hot reservoir = T_h = 950 K

Temperature of the cold reservoir = T_c = 590 K

Maximum theoretical efficiency of the engine = _max

Maximum theoretical efficiency of a heat engine is equal to the carnot efficiency.

_max = 0.379

Energy received by the heat engine from the hot reservoir = Q_h = 790 kJ

Energy the heat engine rejects to the cold reservoir = Q_c = 160 kJ

Work done by the engine = W

Q_h = Q_c + W

790 = 160 + W

W = 630 kJ

Actual efficiency of the engine =

= 0.797

The actual efficiency of the engine is greater than the maximum theoretical efficiency.

This is not possible therefore the given engine is impossible.

a) Maximum theoretical efficiency of the engine = 0.379

b) Actual efficiency of the engine = 0.797

c) The engine is operating impossibly