During the melting of a slab of ice at 273 K at atmospheric pressure
(a) positive work is done by th

Q: Why does the volume of ice decrease when it melts?

Water has a unique property called anomalous expansion. In the solid state (ice), water molecules form a crystalline lattice with a lot of empty space, making it less dense than liquid water. Thus, melting collapses this lattice, reducing the volume.

Q: If the volume decreases, isn't the system doing work?

The system is doing *negative* work on the surroundings because $\Delta V$ is negative. Conversely, the surroundings (atmosphere) are doing *positive* work on the system to compress it.

Q: Does the temperature change during melting?

No, during a phase change like melting at standard atmospheric pressure, the temperature remains constant at $273\text{ K}$ until all the ice has turned into water.

Q: Why does internal energy increase if the temperature is constant?

Internal energy depends on both kinetic and potential energy of molecules. While the constant temperature means the average kinetic energy doesn't change, the heat added breaks the intermolecular bonds, increasing the potential energy of the molecules.

Q: Can we use $\Delta U = n C_v \Delta T$ here?

No, that formula is specifically for ideal gases. For solids and liquids undergoing phase changes, internal energy changes due to latent heat, not just temperature changes.

Question

During the melting of a slab of ice at 273 K at atmospheric pressure

Options:

(A) positive work is done by the ice-water system on the atmosphere

(B) positive work is done on the ice-water system by the atmosphere

(C) the internal energy of the ice-water increases

(D) the internal energy of the ice-water system decreases

Sigma Percentile · Accepted Answer

### The Anomaly of Melting Ice

Imagine a solid block of ice sitting at exactly $273	ext{ K}$ ($0^\circ	ext{C}$) under normal atmospheric pressure. As it begins to melt, it undergoes a phase transition from solid to liquid. This seemingly simple process hides a beautiful thermodynamic anomaly that often catches students off guard.

To melt the ice, heat must be supplied to the system. This means the heat exchange $Q$ is strictly positive ($Q > 0$). But what happens to the volume?

### The Volume Catch

Unlike most substances in the universe, which expand when they melt, water is unique. The crystalline lattice structure of ice contains a lot of empty space, making it less dense than liquid water. Therefore, when ice melts into water, its volume actually **decreases**.

Mathematically, the change in volume is negative: $\Delta V < 0$.

### Work Done: Who is Pushing Whom?

The work done by a system at constant pressure is given by the equation:

$$W_{	ext{by system}} = P \Delta V$$

Since $\Delta V$ is negative, the work done *by* the ice-water system on the atmosphere is negative. What does this mean physically? It means the system is not pushing the atmosphere away; rather, the atmosphere is pushing down on the system, compressing it as it shrinks into water. Thus, **positive work is done on the ice-water system by the atmosphere**.

### The First Law of Thermodynamics

Now, let's bring in the First Law of Thermodynamics to determine the fate of the system's internal energy ($\Delta U$):

$$\Delta U = Q - W_{	ext{by system}}$$

Let's plug in the signs we just deduced. We know that $Q$ is a positive quantity ($+Q$), and $W_{	ext{by system}}$ is a negative quantity ($-|W|$). Substituting these into the First Law yields:

$$\Delta U = (+Q) - (-|W|)$$

$$\Delta U = Q + |W|$$

Because we are adding two positive quantities, the change in internal energy $\Delta U$ must be strictly greater than zero.

### Conclusion

Even though the temperature remains constant at $273	ext{ K}$ during the melting process, the internal energy of the system **increases**. This increase is fueled by both the heat absorbed from the surroundings and the mechanical work done on the system by the atmosphere as it compresses the shrinking volume.

Therefore, the atmosphere does positive work on the system, and the internal energy of the system increases.

Animated Solution for Physics - Thermodynamics: During the melting of a slab of ice at 273 K at atmospheric pressure

Select Answer:

Visualized Solution

Melting of Ice

Heat Absorption

Volume Change

Work Done

First Law of Thermodynamics

Internal Energy Change

Conclusion

The Sigma Insight: First Law of Thermodynamics

The Anomaly of Melting Ice

The Volume Catch

Work Done

The First Law of Thermodynamics

Conclusion

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Animated Solution for Physics - Thermodynamics: During the melting of a slab of ice at 273 K at atmospheric pressure

Select Answer:

Visualized Solution

Melting of Ice

Heat Absorption

Volume Change

Work Done

First Law of Thermodynamics

Internal Energy Change

Conclusion

The Sigma Insight: First Law of Thermodynamics

The Anomaly of Melting Ice

The Volume Catch

Work Done

The First Law of Thermodynamics

Conclusion

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