Question

A heat pump that is used to heat a house has a COP of \(2.5 .\) That is, the heat pump delivers \(2.5 \mathrm{kWh}\) of energy to the house for each \(1 \mathrm{kWh}\) of electricity it consumes. Is this a violation of the first law of thermodynamics? Explain.

Short answer

Answer: No, a heat pump with a COP of 2.5 does not violate the first law of thermodynamics. The heat pump efficiently transfers heat energy from an external source (such as the outside air or ground) to the house using the consumed electrical energy, maintaining the conservation of energy in the process.

Step-by-step solution

Understand COP and the First Law of Thermodynamics

The Coefficient of Performance (COP) of a heat pump measures the efficiency of the system, defined as the ratio of the heat energy output (delivered to the house) to the electrical energy input (consumed by the heat pump). \[ COP =\frac{Energy\; Output}{Energy\; Input} \] The First Law of Thermodynamics states that energy cannot be created or destroyed, only converted from one form to another.

Compute the Total Energy Input and Output

The given heat pump has a COP of 2.5, which means that for every 1 kWh of electricity consumed, it delivers 2.5 kWh of energy to the house. So when the heat pump uses 1 kWh of electrical energy, it transfers 2.5 kWh of heat energy to the house.

Analyze Energy Conservation

According to the first law of thermodynamics, energy cannot be created or destroyed, but it can be converted. Here, the heat pump is converting electrical energy (input) into heat energy (output). When considering the energy conservation principle in this situation, we must account for the fact that the heat pump is not creating energy but is transferring heat from another source (usually from outside air or ground).

Determine If There Is a Violation of the First Law

In the given scenario, we must consider the total energy in the system. The heat pump consumes 1 kWh of electrical energy and delivers 2.5 kWh of heat energy to the house. The additional 1.5 kWh of energy comes from another source (outside air or ground). The total energy input is then 1 kWh (electricity) + 1.5 kWh (from the external source) = 2.5 kWh, equal to the total energy output. Therefore, the conservation of energy is maintained, and the first law of thermodynamics is not violated. In conclusion, the heat pump with a COP of 2.5 is not violating the first law of thermodynamics. The heat pump efficiently transfers heat energy from one source (typically the outside air or ground) to another (inside the house) using the consumed electrical energy.