Question

Find the increase in mass when 1 kg of water is heated from 0°C to 100°C. Specific heat capacity of water = 4200 J kg⁻¹ K⁻¹.

Answer 1

Given:
Mass of water, m = 1 kg
Specific heat capacity of water, s = 4200 J kg⁻¹ K⁻¹
Change in temperature, ∆θ = 100°C

Heat energy required, Q = ms∆θ
Q = 1 × 4200 × 100
= 420000 J

This energy is converted into mass. Thus,
$\mathrm{Increase}\mathrm{in}\mathrm{mass}\mathrm{of}\mathrm{water}\mathrm{on}\mathrm{heating}=∆m=\frac{Q}{c^2}$
$$\begin{gathered} \Rightarrow ∆m=\frac{420000}{{\left(3\times {10}^8\right)}^2} \\ =\frac{42}{9}\times \frac{{10}^4}{{10}^{16}} \\ \Rightarrow ∆m=4.66\times {10}^{-12}\mathrm{kg}\approx 4.7\times {10}^{-12}\mathrm{kg} \end{gathered}$$