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,

Increase in mass of water on heating \[= ∆ m = \frac{Q}{c^2}\]

\[\Rightarrow ∆ m = \frac{420000}{\left( 3 \times {10}^8 \right)^2}\]

\[ = \frac{42}{9} \times \frac{{10}^4}{{10}^{16}}\]

\[ \Rightarrow ∆ m = 4 . 66 \times {10}^{- 12} kg \approx 4 . 7 \times {10}^{- 12} kg\]