For which combination of working temperatures the efficiency of Carnot’s engine is highest

Options

A. 40 K and 20 K
B. 50 K and 30 K
C. 70 K and 50 K
D. 90 K and 60 K

Answer

A

Explanation

For a carnot engine, the efficiency,
`eta=1-T_(2)/T_(1)=(T_(1)-T_(2))/T_(1)`
Thus the efficiency is more if the temperature difference `T_(1) - T_(2)` is more or `T_(1)` is less.
In all the four cases, `T_(1)-T_(2)` is the same. `eta` is the maximum when `T_(1)` is minimum.
`T_(1)` is minimum in option (a) i.e. 40K and 20K.