Worked problem

Refrigeration COP and Compressor Power

Find the compressor input power and the heat rejected at the condenser for a cooling system with a 35 kW evaporator load and a COP of 3.5.

Mechanical, HVAC & Fluids · Last reviewed

Given

A refrigeration system absorbs 35 kW of heat at the evaporator. Its coefficient of performance, defined as cooling effect divided by compressor input power, is 3.5 at these conditions.

Find

The compressor input power, the heat rejected at the condenser, the cooling capacity in tons and the energy efficiency ratio (EER).

Solution

  1. COP = Q(evaporator) ÷ W(compressor), so W = 35 ÷ 3.5 = 10.0 kW.
  2. Energy balance on the cycle: Q(condenser) = Q(evaporator) + W = 35 + 10 = 45 kW.
  3. Capacity = 35 ÷ 3.517 = 9.95 tons.
  4. EER = COP × 3.412 = 3.5 × 3.412 = 11.9 Btu/h per watt.

Answer

10.0 kW compressor | 45 kW rejected at the condenser | 9.95 tons | EER 11.9

What it shows

  • A refrigeration cycle moves heat. The compressor adds work on top of the heat it moves, so the condenser always rejects more heat than the evaporator absorbs.
  • With condenser water that warms by 5 K, the flow is 45 ÷ (4.186 × 5) = 2.15 kg/s, about 2.15 L/s.
  • A lower COP means more power for the same cooling. At COP 3.0, the compressor takes 11.67 kW and the condenser rejects 46.7 kW.

Common mistakes

  • Using the cooling load as the condenser heat rejection. The condenser also rejects the compressor work.
  • Mixing the COP of the compressor alone with the COP of the whole system. Fans, pumps and controls are extra power.
  • Applying one COP at all conditions. COP falls as the condensing temperature rises or the evaporating temperature falls.
  • Using the cooling COP for a heat pump heating duty, where the useful heat is the condenser output.

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

More worked problems

Questions

Can COP be higher than 1?

Yes. COP compares heat moved with work input, and a cycle can move much more heat than the work it takes. That is not a perpetual-motion claim, because the heat is moved, not created.

How do COP and EER relate?

EER is COP expressed in Btu/h per watt, so EER = 3.412 × COP.

Does COP include the fans and pumps?

Only if the definition says so. State what is included whenever you quote a COP.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

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