Internal energy
The internal energy - also called thermodynamic energy - is the total energy contained in a system. It is composed of the thermal energy, chemical energy, nuclear binding energy, as well as interactions between dipoles and external fields. Its change is equal to the sum of the heat which is supplied to a system, and the work which is done on the system. This says the first law of thermodynamics:
Sign: the equation states that the internal energy of a system increases () when it heat or work is fed ( ), since the externally applied energy is stored in the system.
The internal energy is an extensive condition and size as a function of the entropy, the volume and number of particles, a thermodynamic potential.
Definition
Ever more is known about the structure of the material, the more the causes of the internal energy is detected. Physically speaking, we are dealing with a many-body system, which, has a countable sequence of energy values . The internal energy is the thermal average of these energy values:
Where the probabilities are.
Composition
The sum of the position, movement and tension energy is constant for friction-free transactions in a closed system.
- The physico- thermal Share ( thermal energy) rests on all the disordered microscopic motion of molecules - ie on the kinetic energy plus rotational energy plus vibrational energy of molecules -. Well as intermolecular interactions
- The chemical moiety is the potential energy of the binding forces and the binding energy that is contained in the molecules, and for example, a combustion in the form of thermal energy or heat is released.
- The nuclear physics interest describes the potential energy that is present in the nuclei and can be released in nuclear decays, nuclear fission and nuclear fusion.
- In addition, be able to contribute with electric and magnetic external fields nor the interaction of magnetic and electrical elementary dipoles and induced polarization.
Change in thermodynamic processes
A material type ( K = 1)
The First Law of Thermodynamics describes a change in internal energy as the sum of the heat feeds and withdrawals as well as the work done on the corresponding ( closed ) system:
With
- The absolute temperature
- The entropy
- The pressure and
- Volume.
On the right side you write each place because it is not about total differentials as the state variable, but the partial differentials of the process variables and. The last term has a negative sign because an increase in the volume is connected to an output of work.
Integrated:
On any closed path is valid:
Whatever one chooses and the differentials.
Therefore applies to stationary cycles:
Where the indexed with 1 energies are fed (positive) and 2 indexed discharged (negative) (see energy balance for cycles ).
For variable amount of substance and of particles and the chemical potential for the total differential part added (Fundamental equation):
Several grades (K > 1)
Internal energy and its natural variables ( entropy, volume, and amount of substance ) are all extensive state variables. The internal energy changes with a scaling of the thermodynamic system is proportional to the corresponding state variable (S, V) by the proportionality:
With (): number of moles of particles of type.
Such a function is called homogeneous function of the first degree.
By Euler 's theorem and the first law of the Euler equation for the internal energy follows:
Equipartition theorem for ideal gas
For an ideal gas the equipartition theorem applies (internal energy distributed to each degree of freedom each ).
For an ideal gas with three degrees of freedom and particles gives:
Or moles of an ideal gas:
Each with
- - Boltzmann constant
- - Ideal gas constant.