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

No. it is not the violation of the first law of thermodynamics.

Explanation:

Given data

COP = 2.5

Energy delivers = 2.5 KWh

Electricity Consumes = 1 KWh

According to first law of thermodynamics the heat pump takes heat from the lower temperature & then transfer it to the higher temperature by consuming work. in this case also heat is transferred from lower temperature to higher temperature by consuming work so it is not the violation of the first law of thermodynamics.

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