If mass energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

Correct Option: Remain unchanged

Step-by-step Explanation:

When water is cooled to form ice, a phase transition occurs from liquid to solid. During this process, heat energy (specifically, latent heat of fusion) is released by the water to its surroundings.

According to Einstein's mass-energy equivalence relation:

$E=m{c}^2$

This formula suggests that any change in the energy of a system (
$\Delta E$
) must be accompanied by a corresponding change in its mass (
$\Delta m$
), related by:

$\Delta m=\frac{\Delta E}{c^2}$

Here, $c$ represents the speed of light in a vacuum, which is an extremely large value (approximately $3\times {10}^8\text{m/s}$). Because the speed of light squared ($c^2$) is exceedingly vast, the amount of mass equivalent to the released latent heat is virtually negligible.

For example, freezing 1 kg of water releases about $3.34\times {10}^5\text{Joules}$ of energy. The corresponding change in mass is:

$\Delta m=\frac{3.34\times {10}^5}{{(3\times {10}^8)}^2}\approx 3.7\times {10}^{-12}\text{kg}$

Since this mass difference is incredibly tiny and completely undetectable by any experimental means, the total mass of the water during freezing remains unchanged for all practical and physical purposes.