Liquid water at 25^∘ C is introduced into an evacuated,...

Liquid water at $25^{\circ} \mathrm{C}$ is introduced into an evacuated, insulated vessel. Identify the signs of the following thermodynamic functions for the process that occurs: $\Delta H, \Delta S, \Delta T_{\text {water }}, \Delta S_{\text {sum }}, \Delta S_{\text {umiv }}$

Key Concepts

Adiabatic Process

An adiabatic process is one in which no heat is exchanged with the surroundings. In an insulated vessel, the energy changes associated with phase transitions or temperature shifts occur internally. This means that any change in the internal energy, enthalpy, or temperature of the substance is due solely to work or internal conversion of energy from one form to another rather than heat transfer across the system boundaries.

Phase Transition and Vapor?Liquid Equilibrium

When liquid water is placed in an evacuated container, the absence of external pressure forces the water to partially vaporize until a new equilibrium between the liquid and its vapor is achieved. This spontaneous phase transition is a result of the water trying to reach a state where the vapor pressure in the container balances with the conditions in the system, despite the vessel being initially empty.

Latent Heat and Evaporative Cooling

Latent heat is the energy required for a substance to undergo a phase change without a change in temperature at equilibrium. In the case of water evaporating in an adiabatic and evacuated vessel, the latent heat of vaporization is drawn from the liquid itself, causing the remaining liquid to cool. This cooling effect is critical in determining the change in the temperature of the liquid water during the process.

Entropy Change and the Second Law of Thermodynamics

Entropy is a measure of the disorder or randomness of a system, and the second law of thermodynamics states that in an isolated system the total entropy tends to increase for a spontaneous process. As water spontaneously evaporates in the insulated vessel, the overall entropy of the system increases even though the liquid phase may experience a decrease in temperature, highlighting the interplay between microscopic disorder and macroscopic observables.

Thermodynamic State Functions

Thermodynamic functions such as enthalpy (?H), entropy (?S), and temperature (?T) are state functions that provide insight into the energy and disorder changes in the system during a process. The signs of these functions indicate the direction of energy flow or disorder: for instance, a negative ?H might indicate an overall release of heat from the system, while a positive total entropy change (?S_univ) reflects the spontaneous nature of the process in accordance with the second law.

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