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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

Respuesta :

Answer:

[tex]K = 0.076 W/m K[/tex]

Explanation:

Heat required to melt the complete ice is given as

[tex]Q = mL[/tex]

here we have

m = 5.0 kg

[tex]L = 3.35 \times 10^5 J/kg[/tex]

now we have

[tex]Q = (5 kg)(3.35 \times 10^5)[/tex]

[tex]Q = 1.67 \times 10^6 J[/tex]

now the power required to melt ice in 8.4 hours is

[tex]P = \frac{Q}{t} = \frac{1.67\times 10^6}{8.4 \times 3600 s}[/tex]

[tex]P = 55.4 Watt[/tex]

now by formula of conduction we know

[tex]P = \frac{KA(\Delta T)}{x}[/tex]

now we have

[tex]55.4 = \frac{K(0.73 m^2)(25 - 5)}{0.02}[/tex]

[tex]K = 0.076 W/m K[/tex]

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