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

Q: Why don't we notice this mass change in daily life?

The speed of light $c$ is incredibly large ($3 \times 10^8$ m/s). When you divide a small energy change by $c^2$, the resulting mass change is so minuscule that no standard weighing scale can detect it.

Q: Doesn't the law of conservation of mass say mass cannot change?

In classical physics, yes. But in modern physics, mass and energy are a single conserved entity. Mass can convert to energy and vice versa.

Q: Does ice have less mass than the water it was formed from?

Yes, strictly speaking, a block of ice has slightly less mass than the exact same molecules of liquid water at room temperature, because it has less internal energy.

Q: What happens when we melt the ice back into water?

You have to supply heat (energy) to melt the ice. As the system absorbs this energy, its mass increases back to the original value.

Q: Is this the same principle used in nuclear reactors?

Exactly! In nuclear reactions, the mass change is much larger and measurable, which is why they release such enormous amounts of energy.

Question

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

Options:

(A) increase

(B) remain unchanged

(C) decrease

(D) first increase then decrease

Sigma Percentile · Accepted Answer

### The Illusion of Everyday Physics

When we first learn about the physical world, we are taught a comforting, unbreakable rule: **the law of conservation of mass**. If you freeze a kilogram of water, you get exactly a kilogram of ice. Nothing is lost, nothing is gained. It makes perfect intuitive sense.

But what if I told you that this fundamental "truth" is actually a slight illusion? To uncover the real story, we have to zoom out from our everyday experience and look through the lens of modern physics.

### Einstein’s Revolutionary Insight

In 1905, Albert Einstein shattered our classical understanding of the universe with a deceptively simple equation: $$E = mc^2$$.

This equation tells us something profound: **mass and energy are not two separate entities**. They are two sides of the same coin. Mass can be converted into energy, and energy can be converted into mass. They are interconvertible.

Because of this equivalence, any change in the internal energy of a system ($$\Delta E$$) must be accompanied by a proportional change in its mass ($$\Delta m$$). The relationship is given by:

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

### The Thermodynamics of Freezing

Now, let's apply this revolutionary concept to a simple glass of water. Imagine you place water at room temperature into a freezer. As the water cools down and eventually solidifies into ice, what is happening on a thermodynamic level?

The water molecules are slowing down. To transition from a higher-energy liquid state to a lower-energy solid state, the water must release heat into its surroundings. This released heat is known as **latent heat**.

Because the water is giving off heat, it is losing energy. Therefore, the change in the system's energy is negative ($$\Delta E < 0$$).

### The Final Verdict

If the energy of the water decreases, Einstein's equation demands that its mass must also decrease.

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

Since $$\Delta E$$ is a loss, $$\Delta m$$ is also a loss. The mass of the ice is strictly **less** than the mass of the water it was formed from!

Why don't we notice this? The speed of light, $$c$$, is an astronomically large number ($$3 	imes 10^8 	ext{ m/s}$$). When you square it, $$c^2$$ becomes $$9 	imes 10^{16}$$. Dividing a small everyday energy change by this massive number results in a mass change so infinitesimally small that no weighing scale on Earth could ever detect it.

However, the physics is absolute. When water cools to form ice, it loses energy, and therefore, it loses mass. The correct answer is **decrease**.

Animated Solution for Physics - Atoms and Nuclei: If mass-energy equivalence is taken into account, when water is cooled to form ice, the mass of water should

Select Answer:

Visualized Solution

The Physical Process

Mass-Energy Equivalence

Energy Loss During Freezing

Conclusion on Mass

The Way Forward

The Sigma Insight: Nucleus and Nuclear Reaction

The Illusion of Everyday Physics

Einstein’s Revolutionary Insight

The Thermodynamics of Freezing

The Final Verdict

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