Aheat engine is designed to do work. this is possible only if certain relationships between the heats and temperatures at the input and output hold true. which of the following sets of statements must apply for the heat engine to do work?

a) qh < qc and th < tc
b) qh > qc and th < tc
c) qh < qc and th > tc
d) qh > qc and th > tc

part b
find the work w done by the "ideal" heat engine.
express w in terms of qh and qc
w=

part c
the thermal efficiency e of a heat engine is defined as follows: e = w/qh
express the efficiency in terms of qh and qc.
e=

Part A: D

Part B: W = Qh - Qc

Part C: e = 1 - Qc/Qh

Explanation:

The heat engine is the engine that transforms heat (Q) in work (W), and by the second law of the thermodynamics, its efficiency can not be 100%, it means that some heat must be dissipated.

Part A:

The engine works with two sources of heat, one hot (Qh) at a hot temperature (Th) and another cold (Qc) at a cold temperature (Tc). It is necessary so, the hot source will give energy to the fluid of the engine, and the cold source will be the source where these heat will dissipate and the fluid will return to its original temperature. So,

Qh > Qc, and Th > Tc

Part B:

The ideal heat engine is the one that can use the most amount of heat to transform it at work. It is characterized by Qh/Qc = Th/Tc.

The work is the useful energy, so it is the total heat (Qh) less the heat dissipated (Qc):

W = Qh - Qc

Part C:

The effiency is the useful energy divided by the total energy. Because W = Qh - Qc:

e = W/Qh

e = (Qh - Qc)/Qh

e = Qh/Qh - Qc/Qh

e = 1 - Qc/Qh

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