(a) Deduce from the 1 st and 2 nd laws of thermodynamics...

(a) Deduce from the 1 st and 2 nd laws of thermodynamics that, if a substance such as $\mathrm{H}_2 \mathrm{O}$ expands by $0.091 \mathrm{~cm}^3 / \mathrm{g}$ when it freezes, its freezing temperature must decrease with increasing pressure. (b) In an ice-skating rink, skating becomes unpleasant (i.e., falling frequently) if the temperature is too cold so that the ice becomes too hard. Estimate the lowest temperature of the ice on a skating rink for which ice skating for a person of normal weight would be possible and enjoyable. (The latent heat of ice is $80 \mathrm{cal} / \mathrm{g}$ ).

(a) Deduce from the 1 st and 2 nd laws of thermodynamics that, if a substance such as $\mathrm{H}_2 \mathrm{O}$ expands by $0.091 \mathrm{~cm}^3 / \mathrm{g}$ when it freezes, its freezing temperature must decrease with increasing pressure.
(b) In an ice-skating rink, skating becomes unpleasant (i.e., falling frequently) if the temperature is too cold so that the ice becomes too hard. Estimate the lowest temperature of the ice on a skating rink for which ice skating for a person of normal weight would be possible and enjoyable. (The latent heat of ice is $80 \mathrm{cal} / \mathrm{g}$ ).

Key Concepts

Clausius-Clapeyron Equation

This equation provides the relationship between the pressure and temperature along a phase boundary. It quantifies how the phase transition temperature shifts with pressure by incorporating the latent heat and the volume change during the phase transition, thus connecting thermodynamic principles to observable phenomena such as the pressure dependence of the freezing point.

First Law of Thermodynamics

This principle states that energy is conserved in an isolated system, meaning the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. In the context of phase transitions, it is used to relate latent heat to the energy changes involved when a substance changes its state.

Second Law of Thermodynamics

This law establishes that in an isolated system, processes occur in the direction which increases the total entropy, moving towards equilibrium. It is crucial for understanding the natural direction of phase transitions and the dependence of phase equilibrium (such as melting or freezing) on external conditions like pressure.

Latent Heat

Latent heat is the energy absorbed or released during a phase change at constant temperature and pressure. It is a key quantity when relating thermal energy input or output with changes in a substance's state, which in turn influences the temperature at which a phase transition occurs.

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