Heat pump and temperature in the house

[Kuddus]

Homework Statement

A heat pump with COP of 2.5 is used to heat a house. When operating, the heat pump cosumes 8kW of electrical power. If the house is losing heat to the outside at an average rate of 40000 kj/h and the temperature of the house is 3 degree celcius when the heat pump is turned on, determine how long it will take for the temperature in the house to rise to 22 degree celcius. Assume the house is well sealead ( i.e. no airl leaks) and take the entire mass within the house (air, door , furniture , etc) tobe equal to 2000kg of air for which Cv=0.728 kJ/(kg.K) and Cp= 1.005 kJ/(kg.K)

Homework Equations

Cp/Cv=gamma

The Attempt at a Solution

 

[Redbelly98]

Welcome to PF.

I would start by figuring out at what rate the heat pump adds heat to the house.