efficiency

[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]

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.