Molybdenum – Latent Heat of Vaporization – Fusion – Heat Capacity

Specific heat, or specific heat capacity, is a property related to internal energy that is very important in thermodynamics. The intensive properties c_v and c_p are defined for pure, simple compressible substances as partial derivatives of the internal energy u(T, v) and enthalpy h(T, p), respectively:

where the subscripts v and p denote the variables held fixed during differentiation. The properties c_v and c_p are referred to as specific heats(or heat capacities) because under certain special conditions they relate the temperature change of a system to the amount of energy added by heat transfer. Their SI units are J/kg K or J/mol K.

Different substances are affected to different magnitudes by the addition of heat. When a given amount of heat is added to different substances, their temperatures increase by different amounts.

Heat capacity is an extensive property of matter, meaning it is proportional to the size of the system. Heat capacity C has the unit of energy per degree or energy per kelvin. When expressing the same phenomenon as an intensive property, the heat capacity is divided by the amount of substance, mass, or volume, thus the quantity is independent of the size or extent of the sample.

Latent Heat of Vaporization

In general, when a material changes phase from solid to liquid, or from liquid to gas a certain amount of energy is involved in this change of phase. In case of liquid to gas phase change, this amount of energy is known as the enthalpy of vaporization, (symbol ∆H_vap; unit: J) also known as the (latent) heat of vaporization or heat of evaporation. As an example, see the figure, which descibes phase transitions of water.

Latent heat is the amount of heat added to or removed from a substance to produce a change in phase. This energy breaks down the intermolecular attractive forces, and also must provide the energy necessary to expand the gas (the pΔV work). When latent heat is added, no temperature change occurs. The enthalpy of vaporization is a function of the pressure at which that transformation takes place.

The temperature at which vaporization (boiling) starts to occur for a given pressure is also known as the saturation temperature and at this conditions a mixture of vapor and liquid can exist together. The liquid can be said to be saturated with thermal energy. Any addition of thermal energy results in a phase transition. At the boiling point the two phases of a substance, liquid and vapor, have identical free energies and therefore are equally likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the gaseous form is preferred.

Latent Heat of Fusion

In case of solid to liquid phase change, the change in enthalpy required to change its state is known as the enthalpy of fusion, (symbol ∆H_fus; unit: J) also known as the (latent) heat of fusion. Latent heat is the amount of heat added to or removed from a substance to produce a change in phase. This energy breaks down the intermolecular attractive forces, and also must provide the energy necessary to expand the system (the pΔV work).

The liquid phase has a higher internal energy than the solid phase. This means energy must be supplied to a solid in order to melt it and energy is released from a liquid when it freezes, because the molecules in the liquid experience weaker intermolecular forces and so have a higher potential energy (a kind of bond-dissociation energy for intermolecular forces).

The temperature at which the phase transition occurs is the melting point. The melting point also defines a condition in which the solid and liquid can exist in equilibrium. Adding a heat will convert the solid into a liquid with no temperature change. At the melting point the two phases of a substance, liquid and vapor, have identical free energies and therefore are equally likely to exist. Below the melting point, the solid is the more stable state of the two, whereas above the liquid form is preferred. The melting point of a substance depends on pressure and is usually specified at standard pressure. When considered as the temperature of the reverse change from liquid to solid, it is referred to as the freezing point or crystallization point.