Aheat pump has a work input of 2 kw and provides 7 kw of net heat transfer to heat a house. the system is steady, and there are no other work or heat interactions. is this a violation of the first law of thermodynamics? select one: a. yes b. no

No, is not a violation of the first law of thermodynamics.

Explanation:

The first law of thermodynamics states that energy is neither created nor destroyed in an isolated system (a system without mass or energy transfer with ambient).

In a heat pump work is used to transfer heat from a cold body to a hot body (see figure). In a free system heat would go from the heat source to the cold one, that is why you need work. Work and heat are energy in transit.

W + Qin = Qout

In your case

2 kW + Qin =  7 kW

Qin =5 kW

It would be a violation to the first law of thermodynamics if Qout is less than  2 kW.