Determine the increase in mass when 1 kg of water is heated from 0^ C to 100^ C . The specific heat capacity of water is given as 4200 J kg ⁻¹ K ⁻¹ .

Step-by-step solution

The heat energy required to raise the temperature of water is given by Q = mc T . Substituting the given values: Q = 1 4200 100 = 4.2 10^5 J According to Einstein's mass-energy equivalence principle, E = m c^2 . Since the heat supplied increases the internal energy of the water, E = Q . Therefore, the increase in mass is: m = Q c^2 Substituting the values of Q and the speed of light c = 3 10^8 m s ⁻¹ : m = 4.2 10^5 (3 10^8)^2 = 4.2 10^5 9 10¹⁶ m = 0.466 10⁻¹¹ kg 4.7 10⁻¹² kg