Physics - Heat & Thermo Question with Solution | TestHub

A room is to be maintained at ${\mathrm{T}}_{\mathrm{H}}=300\mathrm{K}$ while the outside is at ${\mathrm{T}}_{\mathrm{C}}=270\mathrm{K}$. The heat loss rate from the room is proportional to the temperature difference :

${\mathrm{Q}}_{\mathrm{loss}}=\mathrm{K}\left({\mathrm{T}}_{\mathrm{H}}-{\mathrm{T}}_{\mathrm{C}}\right);\mathrm{K}=500{\mathrm{WK}}^{-1}$

A heat pump supplies heat to the room. Its actual COP is 0.75 times the COP of reversible heat pump operating between ${\mathrm{T}}_{\mathrm{H}}$ and ${\mathrm{T}}_{\mathrm{C}}$. Assuming steady state (the pump exactly compensates the loss), the minimum electrical power input P required (in watts) is :-