A Styrofoam box has a surface area of 0.75 m^2 and a wall thickness of 2.0 cm. T

Question

A Styrofoam box has a surface area of 0.75 m^2 and a wall thickness of 2.0 cm. The temperature of the inner surface is 5.0 degree C, and the outside temperature is 24 degree C. If it takes 8.0 h for 5.0 kg of ice to melt in the container, determine the thermal conductivity of the Styrofoam. A bar of aluminum (bar A) is in thermal contact with a bar of copper (bar B) of the same length and area. One end of the compound bar is maintained at T_h = 80.5 degree C while the opposite end is at 30.0 degree C. Find the temperature at the junction when the energy flow reaches a steady state.

Explanation / Answer

6 ans

Given that

area A=0.75 m^2

thickness L=2*10^-2 m

time t=8 h=8*3600=28800 sec

mass m=5 kg

temperature difference =24-5=19 C

step;2

now we find the coefficient of thermal conductivity

mL/t=KA(T2-T1)/l

5*3.35*10^5/28800=k*0.75*19/2*10^-2

0.582=k*7.125

coefficient of thermal conductivity K=0.082 W/m.k

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7 ans

Given that

temperature at hot end Th=80.5 C

temperature at lower end Tc=30 C

coefficient of thermal conductivity of aluminium K1=205 W/m.k

coefficient of thermal conductivity of copper K2=385 W/m.K

now we find the temperature at junction

the temperature =ThK1+TCK2/K1+K2

=80.5*205+30*385/205+385

=16502.5+8550/590

=42.5 C

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