Determine the increase in mass when 1 kg of water is heated from 0^...

The heat energy required to raise the temperature of water is given by $\Delta Q = mc\Delta T$.

Substituting the given values:

$\Delta Q = 1 \times 4200 \times 100 = 4.2 \times 10^5 \text{ J}$

According to Einstein's mass-energy equivalence principle, $\Delta E = \Delta m c^2$. Since the heat supplied increases the internal energy of the water, $\Delta E = \Delta Q$.

Therefore, the increase in mass is:

$\Delta m = \dfrac{\Delta Q}{c^2}$

Substituting the values of $\Delta Q$ and the speed of light $c = 3 \times 10^8 \text{ m s}^{-1}$:

$\Delta m = \dfrac{4.2 \times 10^5}{(3 \times 10^8)^2} = \dfrac{4.2 \times 10^5}{9 \times 10^{16}}$

$\Delta m = 0.466 \times 10^{-11} \text{ kg} \approx 4.7 \times 10^{-12} \text{ kg}$