Question

6. Find the heat flow in 24 hours through a refrigerator door 30.0" x 58.0" insulated with cellulose fiber 2.0" thick. The temperature inside the refrigerator is 38°F. Room temperature is 72°F. [answer in BTUs]

Answer 1

The heat flow in 24 hours through the refrigerator door is approximately 1,608.57 BTU

Step-by-step explanation:

The given parameters are;

The duration of the heat transfer, t = 24 hours = 86,400 seconds

The area of the refrigerator door, A = 30.0" × 58.0" = 1,740 in.² = 1.122578 m²

The material of the insulator in the door = Cellulose fiber

The thickness of the insulator in the door, d = 2.0" = 0.0508 m

The temperature inside the fridge = 38° F = 276.4833 K

The temperature of the room = 78°F = 298.7056 K

The thermal conductivity of cellulose fiber = 0.040 W/(m·K)

By Fourier's law, the heat flow through a by conduction material is given by the following formula;

`(Q)/(t) = (k \cdot A \cdot (T_2 - T_1) )/(d)`

`Q = (k \cdot A \cdot (T_2 - T_1) )/(d) * t`

Therefore, we have;

`Q = (0.04 * 1.122578 * (298.7056 - 276.4833 ) )/(0.0508) * 86,400 =1,697,131.73522`

The heat flow in 24 hours through the refrigerator door, Q = 1,697,131.73522 J = 1,608.5705140685 BTU