The gradient of the melting line of water on a p-T diagram...

The gradient of the melting line of water on a $p-T$ diagram close to $0^{\circ} \mathrm{C}$ is $-1.4 \times 10^7 \mathrm{~Pa} / \mathrm{K}$. At $0^{\circ} \mathrm{C}$, the specific volume of water is $1.00 \times 10^{-3}$ $\mathrm{m}^3 \mathrm{~kg}^{-1}$ and of ice is $1.09 \times 10^{-3} \mathrm{~m}^3 \mathrm{~kg}^{-1}$. Using this information, deduce the latent heat of fusion of ice.

Key Concepts

Phase Diagram (p-T Diagram)

A phase diagram, particularly a pressure-temperature diagram, is a graphical representation showing the conditions of temperature and pressure under which different phases of a substance (such as solid, liquid, and gas) can coexist. It is crucial for understanding phase equilibria and the effect of external conditions on phase transitions.

Specific Volume

Specific volume is defined as the volume occupied per unit mass of a substance. In the context of phase transitions, differences in specific volumes between phases play a critical role in determining how the phase boundary (e.g., the melting curve) behaves in response to changes in pressure and temperature.

Clapeyron Equation

The Clapeyron equation is a fundamental relation in thermodynamics that links the slope of a phase boundary in a pressure?temperature (p-T) diagram to the enthalpy change and the change in volume during a phase transition. Essentially, it is used to calculate latent heat when the change in specific volume and the gradient of the phase boundary are known.

Latent Heat of Fusion

Latent heat of fusion refers to the amount of energy required to change a substance from a solid to a liquid at constant temperature and pressure, or vice versa, without changing its temperature. It is an important property in phase transition analysis and is directly connected to the energy dynamics during melting or freezing processes.

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