Final answer:
To find the thermal conductivity of the material, we use the heat conduction formula with the known dimensions of the cubical box, the heat transferred, time, and temperature difference between inside and outside the box.
Step-by-step explanation:
The student is asking how to find the thermal conductivity of the material from which a closed box is made, given that a known amount of heat is conducted through the six walls of the box in one day. The box is cubical with a side length of 0.382 m and a wall thickness of 2.87x10-2 m. The temperature difference between the inside and outside is given (-83.3 degrees Celsius inside and 28.9 degrees Celsius outside), and the heat transferred is 3.41 x 106 J.
To find the thermal conductivity (k), we will use the formula for heat conduction: Q = kA(T2 - T1)t/d, where Q is the heat transferred, A is the area through which heat is transferred, T2 - T1 is the temperature difference, t is time, and d is the thickness of the walls. The area (A) for one side of the cubical box is 0.382 m x 0.382 m. Since there are six sides, the total area A = 6 x (0.382 m)2. The time (t) is one day, which is 24 hours or 86400 seconds. Filling in the known values and solving for k gives us the thermal conductivity of the material.