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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.
Since the internal energy of the gas during Joule expansion is constant, cooling must be due to the conversion of internal kinetic energy to internal potential energy, with the opposite being the case for warming. Intermolecular forces are repulsive at short range and attractive at long range (for example, see the Lennard-Jones potential ...
The other equation of state of an ideal gas must express Joule's second law, that the internal energy of a fixed mass of ideal gas is a function only of its temperature, with = (,). For the present purposes it is convenient to postulate an exemplary version of this law by writing:
According to the assumptions of the kinetic theory of ideal gases, one can consider that there are no intermolecular attractions between the molecules, or atoms, of an ideal gas. In other words, its potential energy is zero. Hence, all the energy possessed by the gas is the kinetic energy of the molecules, or atoms, of the gas.
If the calorically perfect gas approximation is used, then the ideal gas law may also be expressed as follows = where is the number density of the gas (number of atoms/molecules per unit volume), = / is the (constant) adiabatic index (ratio of specific heats), = is the internal energy per unit mass (the "specific internal energy"), is the ...
The above derivation uses the first and second laws of thermodynamics. The first law of thermodynamics is essentially a definition of heat, i.e. heat is the change in the internal energy of a system that is not caused by a change of the external parameters of the system.
The internal energy is the sum of thermal kinetic energy and thermal potential energy. [12] Thus, even if the internal energy does not change, the temperature can change due to conversion between kinetic and potential energy; this is what happens in a free expansion and typically produces a decrease in temperature as the fluid expands. [13] [14 ...
The first law of thermodynamics provides the definition of the internal energy of a thermodynamic system, and expresses its change for a closed system in terms of work and heat. [9] It can be linked to the law of conservation of energy. [10]