Answer:
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.