Thermodynamics Problem Solved!

[kolahal_b]

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.

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 engine.

This post has been edited by kolahal_b on Jun 11 2007, 11:30 AM

[Enthalpy]

Another reason:
If you assume one can build a near-ideal Carnot engine, coupling it with the better-than-Carnot refrigerator would create work from nothing.