Answer:
The heat flow in 24 hours through the refrigerator door is approximately 1,608.57 BTU
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;
[tex]\dfrac{Q}{t} = \dfrac{k \cdot A \cdot (T_2 - T_1) }{d}[/tex]
[tex]Q = \dfrac{k \cdot A \cdot (T_2 - T_1) }{d} \times t[/tex]
Therefore, we have;
[tex]Q = \dfrac{0.04 \times 1.122578 \times (298.7056 - 276.4833 ) }{0.0508} \times 86,400 =1,697,131.73522[/tex]
The heat flow in 24 hours through the refrigerator door, Q = 1,697,131.73522 J = 1,608.5705140685 BTU
