Answer to Question #120011 in Physics for Susan Williams

Question

A heating coil of resistance 20 ohms is connected to a 220 V supply for 2 mins to boi a quantity of water in a vessel of heat capacity 100 JK-1. The initial temperature of the water is 400C and its specific heat capacity is 4.2 x 103Jkg-1K-1. calculate the mass of water in the vessel.

Answer 1

Calculate the energy required to boil the mass m of water. The electrical energy $P\tau$ from the heater will heat up the vessel (heat required is $C\Delta t$) and the water (heat required $cm\Delta t$):

$$Q=cm\Delta t+C\Delta t=P\tau,\\ cm\Delta t+C\Delta t=\frac{V^2}{R}\tau,\\\space\\ m=\frac{1}{c}\bigg(\frac{V^2\tau}{R\Delta t}-C\bigg)=\\\space\\ =\frac{1}{4200}\bigg(\frac{220^2\cdot2\cdot60}{20(100-40)}-100\bigg)=1.13\text{ kg}.$$