A ‘thermacole’ icebox is a cheap and efficient method for storing small quantities of

cooked food in summer in particular. A cubical icebox of side 30 cm has a thickness of

5.0 cm. If 4.0 kg of ice is put in the box, what is the amount of ice remaining after 6 h?

The outside temperature is 45 °C, and the coefficient of thermal conductivity of thermacole is $0.01 J s^{-1} m^{-1} K^{-1}.$$\left[Heat of fusion of water=335\times {10}^3 J k{g}^{-1}\right]$

1. 2.9 kg
2. 3.1 kg
3. 3.7 kg
4 4.10 kg

A brass boiler has a base area of \(0.15~\text m^2\) and a thickness of \(1.0 ~\text{cm}.\) It boils water at a rate of \(6.0 ~\text{kg/min}\) when placed on a gas stove. What is the temperature of the part of the flame in contact with the boiler?
(Thermal conductivity of brass \(=109~\text{J s}^{-1}\text{m}^{-1}\text{K}^{-1},\) the heat of vaporization of water \(=2256\times 10^3~\text{J/kg}.\))
1. \(237.98^\circ\text C\)
2. \(150^\circ\text C\)
3. \(137.98^\circ\text C\)
4. \(100^\circ\text C\)