Question

The entropy change can be calculatedby using the expression \(\Delta \mathrm{S}=\frac{\text { Grev }}{\mathrm{T}}\). When water freezes in a glass beaker, choose the correct statement amongs the following : (1) \(\Delta \mathrm{S}_{(\text {system) }}\) decreases but \(\Delta \mathrm{S}_{\text {(surroundings) }}\) remains the same. (2) \(\Delta \mathrm{S}_{\text {(system) }}\) increases but \(\Delta \mathrm{S}_{\text {(surroundings) }}\) decreases. (3) \(\Delta \mathrm{S}_{(\text {system) }}\) decreases but \(\Delta \mathrm{S}_{\text {(surroundings) }}\) increases. (4) \(\Delta \mathrm{S}_{\text {(system) }}\) decreases and \(\Delta \mathrm{S}_{\text {(suroundings) }}\) also decreases.

Short answer

3: \(\Delta S_{system}\) decreases but \(\Delta S_{surroundings}\) increases.

Step-by-step solution

Understand the entropy change formula

The formula given for entropy change is \(\Delta S = \frac{\text{Grev}}{T}\) \where \Delta S \ represents the change in entropy, Grev discusses the reversible heat exchange, and T \ is the absolute temperature in Kelvin. The entropy change in a system (\Delta S_{system}) and surroundings (\Delta S_{surroundings}) need to be considered separately.

Determine the process

When water freezes, it transitions from a less ordered state (liquid) to a more ordered state (solid). This change in state reduces the entropy of the system because ice has a more structured molecular arrangement compared to liquid water.

Analyze the system entropy

Since freezing water reduces the disorder, the entropy of the system decreases. Therefore, \(\Delta S_{system}\) is negative. This matches the criteria mentioned in statements: (1), (3), and (4).

Analyze the surroundings entropy

To maintain the conservation of energy and the second law of thermodynamics, the loss in entropy (\Delta S_{system}) will be transferred to the surroundings, increasing the surroundings' entropy \(\Delta S_{surroundings}\). This fact eliminates statements (1) and (4).

Conclude the correct statement

In the freezing process of water, the correct scenario is \(\Delta S_{system}\) decreases (more ordered structure), while \(\Delta S_{surroundings}\) increases (to conserve overall entropy). This matches statement (3).

Key concepts

second law of thermodynamics

The second law of thermodynamics is a fundamental principle in physics. It states that the total entropy of an isolated system always increases or, at best, remains the same. Entropy is a measure of disorder or randomness. This law implies that natural processes tend to move towards a state of greater disorder.
For example, when water freezes, it moves from a disordered liquid state to an ordered solid state. While the entropy of the water (the system) decreases, the entropy of the surroundings increases to compensate.
This balance keeps the total entropy of the combined system and its surroundings either the same or increased, as predicted by the second law of thermodynamics.

entropy of system

Entropy in a system is a measure of the internal disorder. When discussing a specific system like water freezing, we need to consider how its entropy changes.
During freezing, water molecules arrange in a structured pattern, moving from a higher entropy (liquid) to a lower entropy (solid) state. This reduction in entropy is represented by \(\Delta S_{\mathrm{system}} \), which will be a negative value in this case.
It's crucial to remember that even though the system's entropy decreases, the overall increase in the surroundings' entropy ensures compliance with the second law of thermodynamics.

entropy of surroundings

The entropy of surroundings refers to how changes in a system affect the environment around it.
For instance, when water freezes and its entropy decreases, the surroundings absorb the released heat. This absorption increases the surroundings’ entropy \(\Delta S_{\mathrm{surroundings}} \), ensuring that the total entropy of the universe still upholds the second law of thermodynamics.
It’s a kind of give-and-take: while the system becomes more ordered, the surroundings become slightly more disordered, balancing the scales.