Question

A Styrofoam cooler has a surface area of 2,700 cm2 and a wall thickness of 3.00 cm. Styrofoam has a coefficient of thermal conductivity of 0.010 W/m °C. A 2.00 kg block of ice is placed inside the cooler that has a temperature inside of 2°C. When the temperature outside is 30.0°C, the ice lasts for 8.00 hours. If the temperature outside becomes 20.0°C, then how long will the ice last?

Answer 1

amount of heat transferred Q = K*A*dt*t/l

when the temperature outside = 30

Q = 0.01*2700*10^-4*(30-2)*8*60*60/0.03

when the temperature outside = 20

Q = 0.01*2700*10^-4*(20-2)*x*60*60/0.03

therefore

0.01*2700*10^-4*(20-2)*x*60*60/0.03 = 0.01*2700*10^-4*(30-2)*8*60*60/0.03

x = 12.4 hours