Question

A typical warehouse is built on a cement slap with four walls and a flat roof. The thermal conductivity of the four walls, the roof, and the cement slap are kw, kr, kf with thickness Lw, Lr, Lf respectively. The roof and the cement slap have the same surface area A while the surface of a the wall is 6A. In a hot summer night, the outside air temperature is T_o=120^oF and the ground temperature is T_g=60^oF. The interior of the warehouse is maintained at T_i=70^oF by an air condition unit working continuously. a) Calculate the rate of heat exhausted by the air condition unit. b) Suppose the unit is operated at its maximum efficiency (in a Carnot cycle) with a coefficient of performance E. What is the power consumption of the air condition unit?

Answer 1

This problem can be solved by calculating the total heat flow into the warehouse due to temp difference between inside and outside environment.

Heat flow is given by '

Heat flow between ground

So Total heat flow inside the warehouse is

So Rate of heat exhausted by the Air condition unit is given by

--------------------------------- Solution of part b ----------------------------------------------

coefficient of performance = E which is given by

where Q is the heat removed and W is work done by the unit for that.

So the Power consumption by the air condition unit is given by

this is the power consumption of the air condition unit