`5cm` thick walls of a box like cooler is made of plastic toam. Its total surface area is `1.5m^(2)`. If outside temperature is `30^(@)C`, then how much ice melts each hour inside the cooler to old its temperature at `0^(@)C`.
(Given `K` for plastic `=0.04W//mK, L_(0)=80cal//g` and `1kcal=4.184kJ//kcal`)

Options

A. `4kg`
B. `0.39kg`
C. `3.9kg`
D. `0.2kg`

Explanation

(b) Heat flow into the box `=(DeltaQ)/(Deltat)`
`(DeltaQ)/(Deltat)=KA((DeltaT)/(Deltax))=(0.04)(1.5)(30/0.05)=36W`
`DeltaQ=` In an hour total energy
`=36xx` one hour `=36xx60xx60J=129.6kJ`
`:. DeltaQ=mL=m(80kcal//kg)(4.184kJ//kcal)`
`:.m=(DeltaQ)/(80xx4.184)=129.6/(80xx4.184)kg=0.39kg` ice will melt