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

Answer:

K=24.17 x 10⁻² J s⁻¹c⁻¹m⁻¹

Explanation:

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

$\frac{Q}{t} =\frac{KA\delta T}{d}$

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

$\frac{3.34\times10^6}{6\times86400}= \frac{k\times.011224\times104.7}{4.41\times10^{-2}}$

$K=\frac{3.34\times4.41\times10^4}{6\times86400\times.011224\times104.7}$

K=24.17 x 10⁻² J s⁻¹c⁻¹m⁻¹