Answer to Question #120541 in Physics for Ebose

Question

A heating coil of resistance 20 ohms is connected to a 220 V supply for 2 mins to boil 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

$$Q=Pt=\frac{U^2}{R}t\\Q=mc_w(T'-T)+C(T'-T)\\=(C+c_wm)(T'-T)$$

$$\frac{U^2}{R}t=(C+c_wm)(T'-T)\\\frac{220^2}{20}120=(100+4200m)(100-40)$$

$$m=1.1\ kg$$