Question

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

Short answer

Option (3): $\mathrm{\Delta }{S}_{\text{(system)}}$ decreases but $\mathrm{\Delta }{S}_{\text{(surroundings)}}$ increases.

Step-by-step solution

Understand Entropy Change Formula

The entropy change, $\mathrm{\Delta }S$, is given by $\mathrm{\Delta }\mathrm{S}=\frac{q_{\mathrm{rev}}}{T}$. Here, $q_{\mathrm{rev}}$ is the reversible heat exchange, and $T$ is the absolute temperature.

Identify Process Involved

Freezing of water involves the transition from liquid to solid phase at a constant temperature (0°C or 273 K). During this process, heat is released to the surroundings.

Determine Entropy Change for System

When water freezes, it loses entropy because the molecules become more ordered. Therefore, $\mathrm{\Delta }{S}_{\text{(system)}}$ decreases.

Determine Entropy Change for Surroundings

The heat released by the freezing water is absorbed by the surroundings, increasing their entropy. Therefore, $\mathrm{\Delta }{S}_{\text{(surroundings)}}$ increases.

Correct Statement Selection

Based on the understanding from Steps 3 and 4, the correct statement is (3): $\mathrm{\Delta }{\mathrm{S}}_{\text{(system)}}$ decreases but $\mathrm{\Delta }{\mathrm{S}}_{\text{(surroundings)}}$ increases.

Key concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. It helps in understanding how energy is spread in a process. The formula for entropy change in a thermodynamic process is given by $\mathrm{\Delta }\mathrm{S}=\frac{q_{\mathrm{rev}}}{T}$. Here, $q_{\mathrm{rev}}$ is the reversible heat exchanged by the system and $T$ is the absolute temperature.
When a process occurs, the entropy of the system and the surroundings can change.
In a reversible process, the total entropy change is zero.
But in an irreversible process, the total entropy of the system and surroundings always increases.

Thermodynamics

Thermodynamics is the science of energy and its transformations. It includes the study of heat and work. The first and second laws of thermodynamics are crucial.

• The first law states that energy cannot be created or destroyed, only transferred or converted. It is also known as the law of energy conservation.
• The second law states that in any cyclic process, the entropy of the system either increases or remains constant.

These rules help determine how energy moves and changes in a system.
Understanding thermodynamics is essential in calculating entropy changes during phase transitions and other processes.

Phase Transition

Phase transition refers to the change of a substance from one state of matter to another, such as from liquid to solid.
When water freezes, it undergoes a phase transition from liquid to ice.
During this process, heat is released from the water to the surroundings, and the system's entropy decreases.
However, the surroundings' entropy increases due to the absorbed heat.
In this case, the entropy change formula $\mathrm{\Delta }\mathrm{S}=\frac{q_{\mathrm{rev}}}{T}$ can be used to calculate the entropy change for both the system and the surroundings.
The system becomes more ordered (lower entropy), while the surroundings become less ordered (higher entropy).

Reversible Processes

Reversible processes are ideal, theoretical processes in which the system changes in such a way that the system and surroundings can be returned to their original states without any net change.
These processes are carried out infinitely slowly so that the system is always in thermodynamic equilibrium.
In a reversible process, the total entropy change is zero, meaning the change in the system's entropy is exactly balanced by the change in the surroundings'.
Examples include reversible isothermal expansion of an ideal gas and phase transitions at equilibrium.
Understanding reversible processes helps grasp real-world irreversible processes, where the total entropy always increases.