Question

An ideal heat engine operates of fixed difference of temperatures between hot and cold reservoirs, say 100K. What will provide greater efficiency: operation with the hot reservoir as hot as possible, or operation with a cold reservoir as cold as possible?

Answer 1

To solve this problem we will apply the concepts given for the efficiency of an engine which is given as

`\eta = 1-(T_C)/(T_H)`

`\eta = (T_H-T_C)/(T_H)`

Where

`T_C` = Temperature of the cold reservoir

`T_H` = Temperature of the hot reservoir

The efficiency maximum would be given only if
`T_C = 0`

Replacing this value we have

`\eta = (T_H-0)/(T_H)`

`\eta = 1`

Therefore: Cold reservoir as cold as possible provide the greater efficiency.