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In mathematics and physics, the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. Since then, the heat equation and its variants have been found to be fundamental in ...
The integral heat of dissolution is defined as a process of obtaining a certain amount of solution with a final concentration. The enthalpy change in this process, normalized by the mole number of solute, is evaluated as the molar integral heat of dissolution. Mathematically, the molar integral heat of dissolution is denoted as
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
These effects usually combine to give heat capacities lower than 3R per mole of atoms in the solid, although in molecular solids, heat capacities calculated per mole of molecules in molecular solids may be more than 3R. For example, the heat capacity of water ice at the melting point is about 4.6R per mole of molecules, but only 1.5R per mole ...
Convection (or convective heat transfer) is the transfer of heat from one place to another due to the movement of fluid. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combined processes of conduction (heat diffusion) and advection (heat transfer by bulk fluid flow ).
This equation for the chemical potential can be used as an alternate definition for an ideal solution. However, the vapor above the solution may not actually behave as a mixture of ideal gases. Some authors therefore define an ideal solution as one for which each component obeys the fugacity analogue of Raoult's law f i = x i f i ∗ ...
If the hydration energy is greater than the lattice energy, then the enthalpy of solution is negative (heat is released), otherwise it is positive (heat is absorbed). [3]The hydration energy should not be confused with solvation energy, which is the change in Gibbs free energy (not enthalpy) as solute in the gaseous state is dissolved. [4]
The integral heat of dilution, however, is viewed on a macro scale. With respect to the integral heat, consider a process in which a certain amount of solution diluted from an initial concentration to a final concentration. The enthalpy change in this process, normalized by the mole number of solute, is evaluated as the molar integral heat of ...