An air$-$source$*,$ Carnot heat pump is used to maintain the temperature inside a building at $20C.$

Significantly, the colder it gets outside, the more heat is lost through the walls and windows of the

building. Assume that $85$ kW of heat are lost for each degree difference between the outside and

the inside temperature. That means that the colder it gets, the harder the heat pump will need to

work. However, for safety reasins, the controller circuit for the heat pump limits its electrical power

consumption to $175$ kW $.$ What's the coldest it can get outside before the heat pump cant maintain

the building temperature adequately?

"Air$-$source means that the ambient outdoor air is used as the low$-$temperature reservoir.

$C$