Question

At 1 atm, liquid water is heated above ${100}^{\circ }\mathrm{C}$. For this process, which of the following choices (i-iv) is correct for $\mathrm{\Delta }{S}_{\text{sur }}$ ? $\mathrm{\Delta }S$ ? $\mathrm{\Delta }{S}_{\text{univ }}?$ Explain each answer. i. greater than zero ii. less than zero iii. equal to zero iv. cannot be determined

Short answer

The short answer based on the step-by-step solution is: 1. ∆S_sur: ii. less than zero 2. ∆S: i. greater than zero 3. ∆S_univ: iv. cannot be determined

Step-by-step solution

1. Entropy change of the surroundings (∆S_sur)

For the process of heating liquid water above 100°C, we are adding heat to the system. It means the surroundings are losing heat and becoming more ordered. Therefore, the entropy of the surroundings is decreasing. Hence, the choice for ∆S_sur is: ii. less than zero

2. Entropy change of the system (∆S)

As we heat the liquid water above 100°C, it becomes more disordered since the molecules gain thermal energy, which causes them to move around more. This increases the entropy of the system. Therefore, the choice for ∆S is: i. greater than zero

3. Entropy change of the universe (∆S_univ)

The entropy change of the universe is the sum of the entropy change of the system and the entropy change of the surroundings: ∆S_univ = ∆S + ∆S_sur. Since we have ∆S > 0 and ∆S_sur < 0, it's not possible to determine the sign of ∆S_univ without more information about the specific process to compare the magnitudes of ∆S and ∆S_sur. Therefore, the choice for ∆S_univ is: iv. cannot be determined

Key concepts

Thermodynamics

Thermodynamics is a branch of physics that examines the relationships between heat, work, and energy. It helps us understand how energy is converted from one form to another and how it affects the properties of matter. There are several key principles in thermodynamics:

• Energy Conservation: Energy cannot be created or destroyed, only transformed from one form to another.
• Entropy: A measurement of the disorder or randomness in a system.
• Equilibrium: Systems naturally progress towards a state of equilibrium where energy is evenly distributed.

Thermodynamics plays an essential role in analyzing processes like heating water or powering engines. In this context, when heating water above 100°C, we apply these principles to understand the energy changes and the resulting shifts in entropy.

Entropy change of the system

The entropy change of the system, represented as $\mathrm{\Delta }S$, measures how much the disorder within the system has increased. When liquid water is heated above 100°C, its molecules gain energy and begin to move more freely.
This increased movement translates into greater molecular disorder.

• Molecules have more kinetic energy.
• The arrangement of molecules becomes more random.
• There's an increase in possible microstates.

Thus, the entropy of the system increases, resulting in $\mathrm{\Delta }S$ being greater than zero. It illustrates the second law of thermodynamics, which suggests that systems tend to move towards greater entropy or disorder.

Entropy change of the surroundings

The entropy change of the surroundings, indicated as $\mathrm{\Delta }{S}_{\text{sur}}$, reflects the impact the system has on its environment. When water is heated above 100°C, heat is transferred from an external source to the water. This means the surroundings lose heat.

• The loss of heat leads to less molecular movement in the surroundings.
• Molecules become more ordered as they lose energy.

Therefore, the entropy of the surroundings decreases, resulting in $\mathrm{\Delta }{S}_{\text{sur}}$ being less than zero. This process follows the concept that when energy leaves the surroundings, they're left in a more ordered state.

Entropy change of the universe

The entropy change of the universe, denoted $\mathrm{\Delta }{S}_{\text{univ}}$, is the sum of the entropy changes in both the system and its surroundings:$$\mathrm{\Delta }{S}_{\text{univ}}=\mathrm{\Delta }S+\mathrm{\Delta }{S}_{\text{sur}}$$Since one part increases and the other decreases, determining the net effect requires additional information about the magnitudes of these changes.

• If the increase in the system's entropy is greater, $\mathrm{\Delta }{S}_{\text{univ}}$ will be positive, meaning the overall disorder of the universe increases.
• If the decrease in the surroundings' entropy dominates, $\mathrm{\Delta }{S}_{\text{univ}}$ could be negative.

Without details about the specific amounts of heat transferred, we cannot precisely calculate $\mathrm{\Delta }{S}_{\text{univ}}$. Thus, its change "cannot be determined" directly without additional data.