Question

For a liquid, which would you expect to be larger, \(\Delta S_{\text { fusion }}\) or \(\Delta S_{\text { evaporation }} ?\) Why?

Short answer

For a liquid, we would expect the entropy change during evaporation (\(\Delta S_{\text { evaporation }}\)) to be larger than the entropy change during fusion (\(\Delta S_{\text { fusion }}\)). This is because evaporation involves a much larger increase in disorder compared to fusion, as the substance transitions from a liquid phase to a gaseous phase, which has a significantly higher level of randomness than the liquid phase or solid phases.

Step-by-step solution

1. Understanding Fusion and Evaporation Processes

Fusion is the process where a substance changes from its solid state to its liquid state. Evaporation is the process where a substance changes from its liquid state to its gaseous state. During both these processes, the substance gains energy and undergoes a phase transition.

2. Defining Entropy Change

Entropy (S) is a thermodynamic property that measures the degree of disorder or randomness in a system. The entropy change (ΔS) during a process (such as fusion or evaporation) is the difference between the final entropy of the system and the initial entropy of the system.

3. Entropy Change during Fusion

During the fusion process, a solid absorbs heat and changes into a liquid. As the substance changes from a more ordered solid phase to a more disordered liquid phase, the entropy of the system increases. The entropy change during fusion (ΔS_fusion) can be calculated using the following formula: \[\Delta S_{\text{fusion}} = \frac{q_{\text{fusion}}}{T_{\text{fusion}}}\] where - \(q_{\text{fusion}}\) is the heat absorbed during fusion - \(T_{\text{fusion}}\) is the temperature at which fusion occurs

4. Entropy Change during Evaporation

During the evaporation process, a liquid absorbs heat and changes into a gas. As the substance changes from a more ordered liquid phase to a more disordered gaseous phase, the entropy of the system increases. The entropy change during evaporation (ΔS_evaporation) can be calculated using the following formula: \[\Delta S_{\text{evaporation}} = \frac{q_{\text{evaporation}}}{T_{\text{evaporation}}}\] where - \(q_{\text{evaporation}}\) is the heat absorbed during evaporation - \(T_{\text{evaporation}}\) is the temperature at which evaporation occurs

5. Comparing Entropy Changes

When comparing the two processes, evaporation involves a much larger increase in disorder compared to fusion. In the evaporation process, the substance changes from the liquid phase to the gaseous phase, a state with a significantly higher level of randomness compared to the liquid phase. On the other hand, in fusion, the substance merely changes from the solid phase to the liquid phase, which though is more disordered than the solid phase, is still more ordered than the gaseous phase.

6. Conclusion

Therefore, the entropy change during evaporation (ΔS_evaporation) is larger than the entropy change during fusion (ΔS_fusion) for a liquid. This is because the degree of disorder or randomness is much higher in the gaseous phase compared to the liquid or solid phases.

Key concepts

Phase Transition

Phase transitions refer to the transformation of a substance from one state of matter to another. These states include solid, liquid, and gas. During a phase transition, a substance will change its structure and energy level, typically involving the absorption or release of energy.

• Types of phase transitions include fusion (melting), freezing, evaporation (boiling), condensation, sublimation, and deposition.
• Each transition affects the physical properties of the substance, including temperature, volume, and entropy.

A key factor during these transitions is the role of energy. For example, as a solid heats up and turns into a liquid, or a liquid into a vapor, it's absorbing energy which increases its entropy, or disorder.

Fusion

Fusion, also known as melting, is a phase transition where a solid becomes a liquid. This process occurs when a solid substance absorbs enough heat to overcome its internal forces, allowing its molecules to move more freely.
In terms of energy, the heat absorbed by the solid doesn't increase its temperature during fusion but rather changes the state of matter. The formula for the entropy change during fusion is:\[\Delta S_{\text{fusion}} = \frac{q_{\text{fusion}}}{T_{\text{fusion}}}\]

• Here, \(q_{\text{fusion}}\) is the heat involved in melting the solid.
• \(T_{\text{fusion}}\) is the temperature at which the melting occurs.

Fusion results in an increase in entropy because the molecules in the liquid state are more disordered than those in the solid state. Although increased, this disorder is modest compared to further transitions, like evaporation.

Evaporation

Evaporation is the phase transition where a liquid becomes a gas. It involves the absorption of large amounts of heat, which gives the liquid molecules enough energy to break free into the gaseous state. This transition substantially increases entropy since gases are much more disordered than both solids and liquids.
The entropy change during evaporation is represented by:\[\Delta S_{\text{evaporation}} = \frac{q_{\text{evaporation}}}{T_{\text{evaporation}}}\]

• In this formula, \(q_{\text{evaporation}}\) represents the heat absorbed by the liquid.
• \(T_{\text{evaporation}}\) is the temperature at which evaporation happens.

During evaporation, the increase in randomness or disorder is much greater compared to fusion, reflecting in a larger change in entropy because gases have a higher level of entropy than liquids or solids.

Thermodynamics

Thermodynamics is the branch of physics that studies the relationships between heat, energy, and work. It provides insight into how energy transitions and transformations affect the physical properties of substances through principles and laws.

• The First Law of Thermodynamics, known as the law of energy conservation, states that energy cannot be created or destroyed, only transformed from one form to another.
• The Second Law of Thermodynamics indicates that in any energy transformation, the total entropy (disorder) of a system and its surroundings will increase.

In the context of phase transitions like fusion and evaporation, thermodynamics helps explain why energy absorbed during these processes leads to changes in entropy. The greater the change in disorder, such as in evaporation compared to fusion, the larger the associated entropy change. Understanding these concepts helps predict substance behaviors under different conditions and transitions.