# An FE Exam Problem

1. May 4, 2005

### Naeem

Q. A heat engine cycle is executed with steam in the saturation dome. The pressure of steam is 1 MPa during heat addition and 0.5 MPa during heat rejection. THe highest possible efficiency of the heat engine is.

How to calculate heat efficiency?

W = QH / COP,hp

and

COP = 1 / ( TH /TL - 1 )

Pl. note COP- denotes the coefficient of performance of the heat engine.

Any ideas on how to proceed?

Thanks, a lot!

2. May 4, 2005

### Clausius2

It seems to me that the engine is working with a Rankine Cycle. Anyway, during the change of state the pressure and temperature remains constant. If you have the pressure 1MPa then you have the temperature of saturation of water ($$T_h=180ºC=353K$$) and the pressure 0.5 Mpa gives you $$T_c=150ºC=323K$$ aproximately (verify the data in a table of water).

This means the engine, maybe an steam machine, is vaporizing water in the boiler at temperature $$T_h$$ which may be the hot focus (maybe it is not totally true in a Rankine cycle because the bolier superheats the vapor), and is condensing the vapor at temperature $$T_c$$ in the condenser. The second principle of the thermodynamics states than the maximum efficiency is reached by means of a Carnot engine working between the two extreme temperatures:

$$\eta_{max}=\frac{W}{Q_h}=1-T_c/T_h$$

I don't really understand why you used the COP when we are talking about an engine.