thermodynamic Problem!!

Question

An inventor claims to have developed a novel heat pump that can, when operating steadily, deliver 100 kW of heat to a building at 40°C whilst consuming 10 kW to drive the unit. Assuming that the device is a heat engine and that heat is extracted from the outside atmosphere at -25°C, compare its coefficient of performance with that of a Carnot cycle heat pump and comment on the claim. Explain the basis of your comments.

Answer 1

The coefficient of performance of a heat pump is a ratio of useful heating or cooling provided to work required.

The COP of the pump is, by definition, the Heat Provided/Work Input:

COP_Pump = 100KW/10KW = 10

The COP of a Carnot Cycle Heat Pump operating between two temperatures is:

COP_Carnot = 1/(1-T_L/T_H) = 1/(1-248/313) = 4.815

This is the maximum theoretical COP for any heat pump operating between those two temperatures. Note that the temperature must be in Kelvin, not Celsius.

The COP of our pump is more than double that of a Carnot Cycle operating between the same two temperatures. This is a violation of the 2nd Law of Thermodynamics.