A house located in a city with an outside air temperature of $-3\backslash$deg C is heated with a CARNOT heat pump and maintained at an indoor air temperature of $27\backslash$deg C$.$ The heat loss of the house is $45$ kW$.$ The energy required for the heat pump is provided by a heat engine operating between a $377\backslash$deg C source and $-3\backslash$deg C sink$.$ The thermal efficiency of the heat engine is nth $=0\mathrm{.}35.$a$)$ Calculate the heat QH absorbed from the source at $377\backslash$deg C$.$

b$)$ Find the net waste heat released to the environment at $-3\backslash$deg C $($by the heat pump and engine$).$