Question

Establish a relation between efficiency and coefficient of performance.

Answer 1

Efficiency is the term used where lower grade energy(heat) is being converted into higher grade energy(work) (eg. engines, power plants etc). Since lower grade energy can't be completely converted into higher grade therefore efficiency is always leads than 1.

And vice versa for COP. Since higher grade energy can be completely converted into lower grade energy therefore COP is greater than 1 and tells how effectively the energy conversion is taking place.