Can Any Refrigerator Surpass a Carnot Refrigerator in Efficiency?

[neelakash]

Homework Statement

Show that no refrigerator operating between two reservoirs at a given temperature can have higher co-efficient of performance than a Carnot refrigerator operating between the same two reservoirs.

Homework Equations

The Attempt at a Solution

Please check if I am correct


A perfect refrigerator is one in which no work is required to take heat from the low temperature region to the high temp. region.
This is not possible according to the second law of Thermodynamics
The coefficient of performance of a refrigerator
COP = QL / W
where W = work done
from the first law of thermodynamics we can write
COPideal = QL / ( QH - QL )
= TL / ( TH - TL )
= ( TL / TH) / [ 1 - ( TL / TH) ]
= ( TL / TH) / eideal
= analagous to an ideal Carnot refrigerator

 

[siddharth]

I'd prove this by contradiction.