10 kg of water at 20^∘ C is converted to ice at -10^∘ C by being put in contact with a reservoir

step 1 Hello everyone. This is problem 66 from chapter 18. It says determine the change in entropy that

10 kg of water at 20^∘ C is converted to ice at -10^∘ C by...

10 kg of water at $20^{\circ} \mathrm{C}$ is converted to ice at $-10^{\circ} \mathrm{C}$ by being put in contact with a reservoir at $-10^{\circ} \mathrm{C}$. This process takes place at constant pressure and the heat capacities at constant pressure of water and ice are 4180 and $2090 \mathrm{~J} / \mathrm{kg}$ deg respectively. The heat of fusion of ice is $3.34 \times 10^5 \mathrm{~J} / \mathrm{kg}$. Calculate the change in entropy of the universe.

Key Concepts

Irreversible Processes

Irreversible processes are real processes that involve finite temperature differences, unrestrained heat flow, or other dissipative effects, leading to additional entropy production beyond what is calculated for a reversible process. When a system interacts with a reservoir at a different temperature or undergoes a phase change with finite heat transfer, these irreversible aspects contribute to a net increase in the entropy of the universe. Understanding irreversibility is crucial for accurately determining the total entropy change in practical thermodynamic transformations.

Heat Reservoir

A heat reservoir is an idealized body with a very large thermal capacity that can absorb or supply finite amounts of heat without undergoing a significant change in temperature. In thermodynamic processes, it is used to maintain a constant temperature, simplifying the calculation of entropy changes for the surroundings. Its constant temperature makes it straightforward to compute the entropy change associated with the heat transferred between the system and the reservoir.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to change the temperature of a unit mass of a substance by one degree under constant pressure. This property is essential when calculating the heat exchanged during temperature changes of substances such as water and ice. It allows us to quantify the energy removal or addition needed for cooling or heating processes and is fundamental for integrating the heat input or output over a temperature range during non-phase-change processes.

Entropy Change

Entropy is a measure of the disorder or randomness in a system and quantifies the energy dispersal at a specific temperature. In thermodynamics, the change in entropy for a process is given by the integral of the reversible heat transfer divided by temperature, ?S = ?(dQ/T). When a system undergoes multiple steps, such as cooling, phase change, and further cooling, the overall entropy change is the sum of the entropy changes in each individual phase. This concept is crucial for analyzing the second law of thermodynamics and determining the change in entropy of the universe in irreversible processes.

Latent Heat of Fusion

Latent heat of fusion is the amount of energy per unit mass that must be removed or added to change a substance from a liquid to a solid, or vice versa, at constant temperature and pressure. This energy does not change the temperature but is instead used to overcome the latent energy barrier associated with the phase transition. In the analysis of converting water to ice, the latent heat of fusion determines the heat removal required during the freezing process, impacting the calculation of entropy changes during the phase change.

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