A window-type AC unit which has an 8000 BTU/h power
rating and a COP of 2.5 is used for cooling your home
during a very hot Philly day in August. When you come
back home from school today you realized that you have
forgotten to turn the AC on when you were leaving in the
morning. Now the interior is 32°C while it was supposed to
be 20°C. Also, your old townhouse has bad insulation,
causing the heat to move from outside into the house at a
rate of 5 kW. How long will it take in minutes for this unit to
cool your home to 20°C? Take the volume of the house as
180m$^3$, the density of air 1.2 kg/m$^3$, & Cp of air as 1.005
kJ/kg-K.
Remember: 1 kW = 3,412.14 BTU/h.