There is a heat source, (say a fire next to the engine), which supplies 1000 J o

Question

There is a heat source, (say a fire next to the engine), which supplies 1000 J of heat energy during one cycle and remains at a constant temperature of 400 K. A heat sink, (say the exhaust pipe), exhausts 700 J of heat during a cycle at a constant temperature of 300 K. Both the heat source and sink heat transfers are reversible processes. During one cycle of the engine the engine itself does not change its entropy.

a) How much work can this engine do in one cycle?

b) Calculate the change of entropy of the heat source through one cycle of the engine.

c) Calculate the change of entropy of the heat sink through one cycle of the engine.

d) Does this engine violate the Second Law of Thermodynamics? Why or why not?

e) Describe in your own words what your interpretation of the Second Law of Thermodynamics is.

Include as well the relevance of entropy, number of states and disorder to the Second Law.

Explanation / Answer

1) W = Qin - Qout = 1000 - 700 = 300 J

2) Change of Entropy of Heat Source

S1 = -1000/400 = -2.5 J/K

3) Change of Entropy of Cold Reservoir

S2 = 700/300 = 2.3 J/K

4) Yes. The maximum efficiency of this engine according to the second law is that of the Carnot Engine which is

Max Efficiency = 1 - Tc/Th = 1 - 300/400 = 25%

Efficiency of proposed engine = 300/1000 = 30%

Also by summing the two entropies calculated in 2) and 3), the total is a negative quantity which cannot be.

5) No heat engine can be more efficient than the Carnot Engine. That is one interpretation of the Second Law. An equivalent interpretation is that the total change of entropy for any process is positive, never negative.

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