Igcse Model Questions Vol1 2020 Physics Question 25

An electric kettle rated at \(2.0 \text{ kW}\) is used to heat \(0.5 \text{ kg}\) of water from \(20^{\circ}\!\text{C}\) to its boiling point \(100^{\circ}\!\text{C}\). The kettle's efficiency is \(70\%\). After the water reaches \(100^{\circ}\!\text{C}\) the kettle is switched off and the water cools in a room at \(20^{\circ}\!\text{C}\). The rate of heat loss is proportional to the temperature difference with a constant of proportionality \(5 \text{ W}\!\,^{\circ}\!\text{C}^{-1}\).\n(a) How long does it take to bring the water to the boiling point?\n(b) How long does it take for the water to cool from \(100^{\circ}\!\text{C}\) to \(40^{\circ}\!\text{C}\)? Give your answer for (b) in seconds to three significant figures.