In case of heat engine, efficiency is defined as ratio of workdone (desired paramter from the system) to heat energy supplied. Here impotant criteria is net work done 

In case of a refrigerator ,COP is the ratio of heat absorbed (desired paramter from the sysem ) to work done on the system ,Here the important criteria is heat abosorbed or refrigeration effect.  

The efficiency of a heat pump is meaningless if defined as the net heat transferred divided by the work, as evidenced by this value often being considerably larger than 1. That's why we use the coefficient of performance instead of efficiency. It's basically the same thing as using a different equation for the efficiency of a pump (isentropic work/shaft work) and a turbine (shaft work/isentropic work).

All that parameters compare the desidered effect to the expenses sustained to obtain it. That's all. 

Let us say Q(remove) is the amount of heat removed from a space, Q(reject) be the heat rejected to another space and the work done is W (energy input to the equipment) during a process.

Then a conservation of energy equation will give

Q(reject) = Q(remove) + W

COP is a contextual dimensionless ratio to state the performance of an equipment or process.

Broadly, COP is defined as a ratio of  Desired Output/Required Input (recall energy efficiency is also similar ---- Work Output/Heat Input).

For refrigeration: (required is cooling effect (Desired))

The measure of efficiency of the equipment will be COP (for refrigeration) = Q(remove)/W

How much quantity of heat can be removed per unit energy input.

For Heat pumps: (required is heating effect (Desired))

COP(heat pumps) = Q(reject)/W ----- (This will be greater than 1 always !)

How much heating effect is added to a space per unit energy input.

For Mechanical equipment:

Work out put is required (desired) for a given energy (fuel, electricity) input. This gives a ratio known as thermal efficiency = Work output/Energy input.

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Simply speaking, thermal efficiency is a subset of a larger term COP !

In refrigerators and heat pumps the performance is measured by COP which is desired effect divided by the net work done. The desired effect may be heating effect in case of heat pump or cooling effect in case of refrigerator. The desired effect indicates the amount of heat added or removed to maintain the body at a certain temperature.

While in case of heat engine efficiency becomes important which is net work output divided by the amount of heat supplied. Thus giving an idea about the amount of energy supplied which is converted to the work output. 

In heat engine, efficiency is a conversion factor, it is a measure of how much heat energy (input) converted to mechanical or electrical energy (output), however, this is not the case in refrigeration, where the input energy (mechanical for example) is applied to make energy transfers from the cooled space (low temperature reservoir) to  refrigerant. In other words, we do not see energy output in refrigeration system, where both energies mechanical to compressor and heat to evaporator are input energy. That is why people prefere to use another factor rather than efficiency to express the performance of refrigeration systems, and they call it Coefficient of performance.

In the case of heat engines, the cycle can be explained as follows: energy transfers from high temperature reservoir to low temperature one and finally mechanical work is produced. The performance for such systems is measured as the ratio of the work done (desired energy) to the energy input as a heat source (energy that costs). This parameter, which called efficiency, can not exceed unity because at any point the output will never exceeds the energy input, otherwise the thermodynamic laws destroy. For the heat pumps (cooling or heating), the cycle will be reversed, the heat energy transfers from low temperature reservoir to high temperature one. This cannot be done unless external mechanical work (compressor work) is applied. Here, the ratio of the desired energy (heat absorbed in refrigeration) to the energy that costs (compressor work) exceeds unity, and called the COP, is the measure of the heat pumps performance.

It is possible de get an efficiency (ranging between 0 and 1) for refrigeration and heat pump systems. You need just to do an exergy analysis. In an exergy analysis, it is possible to calculate exergy losses, exergy efficiencies for each process and the exergy efficiency of the whole system. An efficiency (0-1) is more meaningful than COP for an engineer

Dear Vishal, Efficiency is a measure of how best of a system can transform forms of energy input into output mechanical workdone. For heat engines, the mechanical work is an output and therefore thermal efficiency is defined as a ratio of net mechanical work output to heat Input. However, for the heat pumps and refrigerators, the mechanical work is an input into th system.

Unlike for efficiency, the COP is defined as a ratio of Heat Input (absorbed) to mechanical work input (or commonly defined as cooling capacity divided by power absorbed). Suppose the mechanical work input (for pump/compressor) was replaced by heat energy like in the case of absorption refrigerators, then the COP becomes just ratio of Heat Absorbed to Heat Input.  To say the least, the COP is not the same as Efficiency although both are measures of systems' performance.

In heat engines the used out put is part of the payed for input, this gives the efficiency to be less than 100% always.

in case of refrigeration or heat pump, the used out put is not part of the payed for input, this gives free value for that ratio to be lower or higher than 100%. it was called COP

Hello Vishal,

it is only a convention. For direct (engines) or indirect (refrigerator/heat pump) energy conversion systems the definition is:

Desired Output/Required Input

In this way the end-user can estimate the output from the input just by multiplying them.

As a consequence of this choice the limits allowed by first and second laws of thermodynamics are different for each case.

If you need more, please ask

Alfonso WIlliam Mauro

thanks a lot everyone for your valuable answers.

Efficiency is a dimensionless obtained by dividing two quantities of same units. The Coefficient of Performance (COP) can depend on numerous other variables and can be used to easily compare the performance of two different units, or the same unit under different conditions.

Both efficiency and COP are dimensionless parameters expressing the ratio between the desired effect and the related cost to sustain. Efficiency is normalized because the effect is always lower than the related cost. This is not the case for the COP or the EER.