How to calculate the efficiency of anything

[daisyi]

The boiler of a steam engine produces steam at a temperature of 500C. The engine exhausts its waste heat into the atmosphere where the temperature is 20C. Assuming that the efficiency of an engine can never be greater than that of a Carnot engine, what is the limiting efficiency of this engine?

I don't even know where to start with this one, I'm not sure that I understand how to calculate the efficiency of anything unless I know that it is a Carnot cycle or an Otto cycle.

 

[Doc Al]

Carnot cycle efficiency

I don't even know where to start with this one, I'm not sure that I understand how to calculate the efficiency of anything unless I know that it is a Carnot cycle or an Otto cycle.

Since you are trying to find the limiting efficiency, treat it as a Carnot cycle. The efficiency of a Carnot cycle (which assumes an ideal reversible process) is:
$$\eta = \frac{T_{hot}-T_{cold}}{T_{hot}}$$

where the temperatures are in degrees K.

 

[M98Ranger]

If this is referring to the efficiency of a steam engine, then the efficiency would be calculated by taking the work output of the engine divided by the heat input. In this case, the work output would be the mechanical work of the engine and the heat input would be the energy produced by the boiler. However, the efficiency of an engine can never be greater than that of a Carnot engine, which is the most efficient heat engine possible. The efficiency of a Carnot engine is calculated by taking the difference in temperature between the hot and cold reservoirs (in this case, 500C and 20C) and dividing it by the temperature of the hot reservoir (500C). So, the limiting efficiency of this engine would be (500C-20C)/500C, which equals 0.96 or 96%. This means that the efficiency of this engine cannot be greater than 96%.