Can Refrigerators Have Greater Efficiency Than Theoretical Value?

[Chronos000]

Homework Statement

the efficiency of a fridge is given by n=Q/W but this is actually the coefficient of performance.

normally the efficiency of an engine is n= W/Q.

the result i get for the coefficient of performance is 18.5 and my textbook says real fridges have coefficients of 4 or 5. you would think one over this value would give the actual efficiency. but if you do this then the efficiency of real fridges is greater than the theoretical one.

I clearly don't understand something here. also, can i derive the specific solution for any engine/fridge from a general form?

 

[vela]

The measure of efficiency is always output/input. In the case of the engine, you're taking heat Q from the hot reservoir and produce work W, so the efficiency is W/Q. In the case of the refrigerator (no D in refrigerator!), you're doing work W for the goal of removing heat Q from the cold reservoir, so the coefficient of performance is Q/W.

 

[Chronos000]

that makes sense. so the idea of getting a percentage efficiency doesn't exist for a fridge?

 

[Chronos000]

and I was sure I'd spelt it wrong haha

 

[vela]

Right. But you could compare a real refrigerator to a Carnot refrigerator working between the same two temperature reservoirs. The Carnot refrigerator would extract the most heat for a given amount of work, so the fraction Q_real/Q_Carnot could be seen as a percentage efficiency, in the sense it measures how close the real refrigerator gets to being an ideal one.

 

[Chronos000]

thats great, thanks