Suppose we vaporize a mole of liquid water at 25^∘ C and another mole of water at 100 ^∘ C. (a)

step 1 We're asked about two different vaporizations, both for water but at different temperatures. One

Suppose we vaporize a mole of liquid water at 25^∘ C and...

Suppose we vaporize a mole of liquid water at $25^{\circ} \mathrm{C}$ and another mole of water at $100{ }^{\circ} \mathrm{C}$. (a) Assuming that the enthalpy of vaporization of water does not change much between $25^{\circ} \mathrm{C}$ and $100^{\circ} \mathrm{C},$ which process involves the larger change in entropy? (b) Does the entropy change in either process depend on whether we carry out the process reversibly or not? Explain.

Key Concepts

Entropy Change in Phase Transitions

This concept involves understanding that during a phase transition, such as vaporization of a liquid to gas, the system undergoes a significant increase in disorder, reflected in an increase in entropy. The change in entropy for the transition can be approximated by the formula ?S = ?H_vap/T, where ?H_vap is the enthalpy of vaporization and T is the absolute temperature. This relationship highlights how the same enthalpy change leads to different entropy changes when the process occurs at different temperatures.

Temperature Dependence of Entropy Change

The role of temperature is crucial in determining the magnitude of the entropy change associated with a phase transition. Since the expression ?S = ?H_vap/T shows that entropy change is inversely proportional to the temperature, vaporizing water at a lower temperature (like 25°C) results in a larger increase in entropy compared to vaporizing at a higher temperature (such as 100°C), assuming the enthalpy of vaporization remains nearly constant.

Reversible vs Irreversible Processes

In thermodynamics, the entropy change of a system during a phase change is determined solely by the initial and final states, and is given by a state function calculation. Therefore, regardless of whether the process is carried out reversibly or irreversibly, the total change in entropy for the system remains the same. However, the overall entropy change, including that of the surroundings, would differ based on the reversibility of the process.

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