Question

Q4 . Consider a heat engine which does 500 MJ of work over a 3 hour period and operates between a hot reservoir of Th = 1250 C and a cold reservoir of Tc = 30.0 C. The engine is ideal and therefore running at its maximum efficiency.

a) [4 marks] Show that the efficiency is 80.0%?

b) [6 marks] How much heat: a. Comes from the hot reservoir? b. Is added to the cold reservoir?

c) [5 marks] What is the rate of entropy change of the hot reservoir?

d) [5 marks] Comment, with reasons, on the effect this engine has on the entropy of the surrounding universe.

Answer 1

a) The formula for the efficiency is:

b) To calculate the heat at the hot reservoir, using the formula for the efficiency,

So, the heat at the cold reservoir will be:

c) The rate of entropy change in the hot reservoir is:

d) Since the heat is coming out from the hot reservoir and going to the surrounding Universe, the heat energy of the Universe will increase, and therefore, the entropy of the Universe will also increase.