**(3)**

Internal energy is the sum of all microscopic forms of energy of a system. It is the energy needed to create the system. It is related to the potential energy, e.g., molecular structure, crystal structure, and other geometric aspects, as well as the motion of the particles, in form of kinetic energy. Thermodynamics is chiefly concerned with changes in internal energy and not its absolute value, which is impossible to determine with thermodynamics alone.^{[17]}

**(3)**

Internal energy is the sum of all microscopic forms of energy of a system. It is the energy needed to create the system. It is related to the potential energy, e.g., molecular structure, crystal structure, and other geometric aspects, as well as the motion of the particles, in form of kinetic energy. Thermodynamics is chiefly concerned with changes in internal energy and not its absolute value, which is impossible to determine with thermodynamics alone.^{[17]}

The fir

The first law of thermodynamics asserts that energy (but not necessarily thermodynamic free energy) is always conserved^{[18]} and that heat flow is a form of energy transfer. For homogeneous systems, with a well-defined temperature and pressure, a commonly used corollary of the first law is that, for a system subject only to pressure forces and heat transfer (e.g., a cylinder-full of gas) without chemical changes, the differential change in the internal energy of the system (with a *gain* in energy signified by a positive quantity) is given as

- where the first term on the right is the heat transferred into the system, expressed in terms of temperature
*T*and entropy*S*(in which entropy increases and the change d*S*is positive when the system is heated), and the last term on the right hand side is identified as work done on the system, where pressure is*P*and volume*V*(the negative sign results since compression of the system requires work to be done on it and so the volume change, d*V*, is negative when work is done on the system).This equation is highly specific, ignoring all chemical, electrical, nuclear, and gravitational forces, effects such as advection of any form of energy other than heat and pV-work. The general formulation of the first law (i.e., conservation of energy) is valid even in situations in which the system is not homogeneous. For these cases the change in internal energy of a

*closed*system is expressed in a general form by*closed*system is expressed in a general form bywhere is the heat supplied to the system and is the work applied to the system.

### Equipartition of energy

The energy of a mechanical harmonic oscillator (a mass on a spring) is alternatively kinetic and potential energy. At two points in the oscillation cycle it is entirely kinetic, and at two points it is entirely potential. Over the whole cycle, or over many cycles, net energy is thus equally split between kinetic and potential. This is called equipartition principle; total energy of a system with many degrees of freedom is equally split among all available degrees of freedom.

This principle is vitally important to understanding the behaviour of a quantity closely related to energy, called harmonic oscillator (a mass on a spring) is alternatively kinetic and potential energy. At two points in the oscillation cycle it is entirely kinetic, and at two points it is entirely potential. Over the whole cycle, or over many cycles, net energy is thus equally split between kinetic and potential. This is called equipartition principle; total energy of a system with many degrees of freedom is equally split among all available degrees of freedom.

This principle is vitally important to understanding the behaviour of a quantity closely rela

This principle is vitally important to understanding the behaviour of a quantity closely related to energy, called entropy. Entropy is a measure of evenness of a distribution of energy between parts of a system. When an isolated system is given more degrees of freedom (i.e., given new available energy states that are the same as existing states), then total energy spreads over all available degrees equally without distinction between "new" and "old" degrees. This mathematical result is called the second law of thermodynamics. The second law of thermodynamics is valid only for systems which are near or in equilibrium state. For non-equilibrium systems, the laws governing system's behavior are still debatable. One of the guiding principles for these systems is the principle of maximum entropy production.

^{[19]}^{[20]}It states that nonequilibrium systems behave in such a way to maximize its entropy production.^{[21]}