Problem 3.
A 1.8 m wide by 1.0 m tall by 0.65m deep home freezer is insulated with 5.0cm thick Styrofoam insulation. At what rate must the compressor remove heat from the freezer to keep the inside at (-20°C) in a room where the air temperature is 25°C.

143.352 watt.

Explanation:

So, in the question above we are given the following parameters or data or information that is going to assist us in answering the question above efficiently. The parameters are:

"A 1.8 m wide by 1.0 m tall by 0.65m deep home freezer is insulated with 5.0cm thick Styrofoam insulation"

The inside temperature of the freezer = -20°C.

Thickness = 5.0cm = 5.0 × 10^-2 m.

Step one: Calculate the surface area of the freezer. That can be done by using the formula below:

Area = 2[ ( Length × breadth) + (breadth × height) + (length × height) ].

Area = 2[ (1.8 × 0.65) + (0.65 × 1.0) + (1.8 × 1.0)].

Area = 7.24 m^2.

Step two: Calculate the rate of heat transfer by using the formula below;

Rate of heat transfer =[ thermal conductivity × Area (T1 - T2) ]/ thickness.

Rate of heat transfer = 0.022 × 7.24(25+20)/5.0 × 10^-2 = 143.352 watt.