Question

A Styrofoam box has a surface area of 0.73 m and a wall thickness of 2.0 cm. The temperature of the inner surface is 5.0°C, and the outside temperature is 25°C. If it takes 8.4 h for 5.0 kg of ice to melt in the container, determine the thermal conductivity of the Styrofoam W/m-K

Answer 1

Answer:

$K = 0.076 W/m K$

Explanation:

Heat required to melt the complete ice is given as

$Q = mL$

here we have

m = 5.0 kg

$L = 3.35 \times 10^5 J/kg$

now we have

$Q = (5 kg)(3.35 \times 10^5)$

$Q = 1.67 \times 10^6 J$

now the power required to melt ice in 8.4 hours is

$P = \frac{Q}{t} = \frac{1.67\times 10^6}{8.4 \times 3600 s}$

$P = 55.4 Watt$

now by formula of conduction we know

$P = \frac{KA(\Delta T)}{x}$

now we have

$55.4 = \frac{K(0.73 m^2)(25 - 5)}{0.02}$

$K = 0.076 W/m K$