Question

A closed box is filled with dry ice at a temperature of -94.9 oC, while the outside temperature is 23.8 oC. The box is cubical, measuring 0.368 m on a side, and the thickness of the walls is 2.96 × 10-2 m. In one day, 3.76 × 106 J of heat is conducted through the six walls. Find the thermal conductivity of the material from which the box is made.

Answer 1

here,

temperature of ice, ti = -94.9 C

outside temperature, to = 23.8 C

side of box, s = 0.369 m

thickness, t = 0.0296 m

heat, Q = 3.76*10^6 J

Net area of box, A = 0.369^2 * 6 = 0.817 m^2

time interval, time = 1 day * 24 * 3600 = 86400 s

heat transmitted per unit area
Q/A = 3.76 * 10^6 / 0.817
Q/A = 4602203.182 J/m^2

Temperature difference, del(t) = (23.8 - (-94.9)) = 118.7 K

therefore :

thermal conductivity = heat per unit area / (del(t) * time * thickness)

thermal conductivity = 4602203.182 / (118.7 * 86400 * 0.0296)

thermal conductivity = 15.16 W / mK