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The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable, a thermodynamic potential, and an extensive property. [5] Thermodynamics defines internal energy macroscopically, for the body as a whole.
Just as a small increment of energy in a mechanical system is the product of a force times a small displacement, so an increment in the energy of a thermodynamic system can be expressed as the sum of the products of certain generalized "forces" which, when unbalanced, cause certain generalized "displacements" to occur, with their product being the energy transferred as a result.
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 ...
This definition can be derived from the microcanonical ensemble, which is a system of a constant number of particles, a constant volume and that does not exchange energy with its environment. Suppose that the system has some external parameter, x, that can be changed. In general, the energy eigenstates of the system will depend on x.
Here is the number of moles of gas and is the molar ideal gas constant. Because the internal energy does not change and the internal energy of an ideal gas is solely a function of temperature, the temperature of the gas does not change; therefore =.
where W is work, U is internal energy, and Q is heat. [1] Pressure-volume work by the closed system is defined as: = where Δ means change over the whole process, whereas d denotes a differential. Since pressure is constant, this means that =. Applying the ideal gas law, this becomes
The equilibrium state of a thermodynamic system is described by specifying its "state". The state of a thermodynamic system is specified by a number of extensive quantities, the most familiar of which are volume, internal energy, and the amount of each constituent particle (particle numbers). Extensive parameters are properties of the entire ...
Internal pressure can be expressed in terms of temperature, pressure and their mutual dependence: = This equation is one of the simplest thermodynamic equations.More precisely, it is a thermodynamic property relation, since it holds true for any system and connects the equation of state to one or more thermodynamic energy properties.