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 \(\Delta S_{\text {surr }}\) ? \(\Delta S ?\) \(\Delta S_{\text {univ }}\) ? Explain each answer. i. greater than zero ii. less than zero iii. equal to zero iv. cannot be determined

Short answer

In this process, ΔS of the system is greater than zero (option i) because the phase change from liquid water to water vapor increases disorder. The ΔS_surr is less than zero (option ii) because the surroundings lose heat, leading to decreased disorder. The ΔS_univ cannot be determined without more information (option iv), as it depends on the magnitudes of ΔS and ΔS_surr.

Step-by-step solution

Understand the given situation and definitions

As liquid water is heated above 100°C, it will undergo a phase change and become water vapor (steam). This is important to consider when determining the changes in entropy. Entropy (S) is a measure of the disorder or randomness in a system. During a process, there are three possible changes in entropy: (i) ΔS > 0 (entropy increases), (ii) ΔS < 0 (entropy decreases), and (iii) ΔS = 0 (entropy remains constant). Now we will analyze the changes in entropy for the system, surroundings, and universe.

Entropy change for the system (ΔS)

For the system which is heating the liquid water, the entropy change is a result of a phase transition: liquid water turning into water vapor. This change of phase increases the disorder of the system because water molecules in the vapor phase are more disordered than they are in the liquid phase. This means that the entropy change for the system (ΔS) is greater than zero (positive).

Entropy change for the surroundings (ΔS_surr)

The surroundings of the system are losing heat to the system, as heat flows from the surroundings into the system to heat the liquid water. As a result, the entropy of the surroundings decreases, because the energy (heat) that has left the surroundings causes less disorder. Therefore, the entropy change for the surroundings (ΔS_surr) is less than zero (negative).

Determine the entropy change for the universe (ΔS_univ)

The entropy change for the universe (ΔS_univ) is the sum of the entropy changes for the system and the surroundings: ΔS_univ = ΔS + ΔS_surr. Since ΔS is positive (greater than zero) and ΔS_surr is negative (less than zero), the overall entropy change for the universe depends on whether the magnitude of the positive entropy change (ΔS) is greater than, equal to, or less than the magnitude of the negative entropy change (ΔS_surr). If the magnitudes are equal, then ΔS_univ = 0. If the magnitude of ΔS is greater than the magnitude of ΔS_surr, then ΔS_univ > 0. And if the magnitude of ΔS is less than the magnitude of ΔS_surr, then ΔS_univ < 0.

Find the correct option for the given situation

Now we can determine which of the given options (i-iv) is correct for the changes in entropy: ΔS_surr: less than zero (option ii) ΔS: greater than zero (option i) ΔS_univ: cannot be determined without more information (option iv) In conclusion, the correct option for ΔS_surr is less than zero, for ΔS is greater than zero, and for ΔS_univ is that it cannot be determined with the given information.

Key concepts

Phase Change

When water is heated above its boiling point at 1 atm, it undergoes a phase change from liquid to vapor. This transition involves energy, often in the form of heat, to break the intermolecular forces binding the liquid molecules. During this process, water molecules become more disordered because they are moving more freely in the vapor phase. This increase in disorder translates to an increase in entropy \((\Delta S)\). Phase changes are fascinating because they illustrate the transition between more ordered and less ordered states. The boiling of water, for example, underscores the significant increase in entropy as molecules escape the constraints of their liquid state.

System and Surroundings

In the study of thermodynamics, the concepts of system and surroundings are crucial. The system refers to the part of the universe that is being studied, while the surroundings include everything else outside the system. In our scenario, the system is the water being heated, and the surroundings are the environment supplying the heat.

• When heat flows into the system (water), the surroundings lose this heat.
• As a result, the entropy of the surroundings \((\Delta S_{\text{surr}})\) decreases because there is less energy and therefore less disorder.

Understanding these interactions helps in analyzing energy changes and their impacts, emphasizing how interconnected the system and its environment are.

Second Law of Thermodynamics

The Second Law of Thermodynamics states that the total entropy of an isolated system can never decrease over time. In simple terms, it means that the overall disorder tends to increase. For any spontaneous process, such as boiling water, the change in entropy of the universe \((\Delta S_{\text{univ}})\) is considered. This is the sum of the entropy changes in the system and surroundings: \[ \Delta S_{\text{univ}} = \Delta S + \Delta S_{\text{surr}} \]

• If \(\Delta S_{\text{univ}}\) is positive, the process is spontaneous, and entropy increases.
• If \(\Delta S_{\text{univ}}\) is zero, the system is in equilibrium.
• In this scenario, without knowing all factors, \(\Delta S_{\text{univ}}\) cannot be precisely determined, illustrating the need for a complete understanding of all energy exchanges.

This law guides us in predicting the direction of natural processes and understanding that energy dispersal tends towards greater entropy.