Question

A closed box is filled with dry ice at a temperature of -87.1°C, while the outside temperature is 17.6°C. The box is cubical, measuring 0.332 m on a side, and the thickness of the walls is 4.41 × 10^-2 m. In one day, 3.34 × 10^6 J of heat is conducted through the six walls. Find the thermal conductivity of the material from which the box is made.

Answer 1

K=24.17 x 10⁻² J s⁻¹c⁻¹m⁻¹

Step-by-step explanation:

Rate of flow of heat through a material is given by the following expression

`(Q)/(t) =(KA\delta T)/(d)`

where Q is amount of heat flowing in time t through area A and a medium of thickness d having two faces at temperature difference δT . K is thermal conductivity of the medium .

Here Q = 3.34 x 10⁶/6 , t = 24 x 60 x 60 = 86400 s , A = .332 X .332 = .0110224 m² , δT = 104.7

Put these values here

`(3.34*10^6)/(6*86400)= (k*.011224*104.7)/(4.41*10^(-2))`

`K=(3.34*4.41*10^4)/(6*86400*.011224*104.7)`

K=24.17 x 10⁻² J s⁻¹c⁻¹m⁻¹