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Breaking and making chemical bonds involves energy release or uptake, often as heat that may be either absorbed by or evolved from the chemical system. Energy released (or absorbed) because of a reaction between chemical substances ("reactants") is equal to the difference between the energy content of the products and the reactants.
The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization.
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".
The relation is generally expressed as a microscopic change in internal energy in terms of microscopic changes in entropy, and volume for a closed system in thermal equilibrium in the following way. d U = T d S − P d V {\displaystyle \mathrm {d} U=T\,\mathrm {d} S-P\,\mathrm {d} V\,}
For example, in many cases of such evolution, internal mechanical equilibrium is established much more rapidly than the other aspects of the eventual thermodynamic equilibrium. [57] Another example is that, in many cases of such evolution, thermal equilibrium is reached much more rapidly than chemical equilibrium. [60]
Each pair in the equation are known as a conjugate pair with respect to the internal energy. The intensive variables may be viewed as a generalized "force". An imbalance in the intensive variable will cause a "flow" of the extensive variable in a direction to counter the imbalance. The equation may be seen as a particular case of the chain rule.
Defining equation SI unit Dimension Temperature gradient: No standard symbol K⋅m −1: ΘL −1: Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer P = / W ML 2 T −3: Thermal intensity I = / W⋅m −2
Such thermal energy manifests itself, however, in changes in the non-chemical state variables (such as temperature, pressure, volume) of the joint systems, as well as the changes in the mole numbers of the chemical constituents that describe the chemical reaction. [citation needed] Internal energy is defined with respect to some standard state.