# Formula Ideal Gas Internal energy Degrees of freedom Temperature Stoffmenge

## Internal energy

`$$ U $$`Unit

`$$ \mathrm{J} $$`

Internal energy is the total energy of molecules or atoms of an ideal gas that is in thermodynamic equilibrium.

## Degrees of freedom

`$$ f $$`Unit

`$$ - $$`

Number of degrees of freedom of a particle of the gas. In the three-dimensional case and without particles being able to rotate and vibrate, \( f = 3 \). The more degrees of freedom the gas has, the greater the internal energy of the system.

## Temperature

`$$ T $$`Unit

`$$ \mathrm{K} $$`

Absolute temperature of the system, that is the temperature of a gas. The greater the temperature, the greater the internal energy.

## Stoffmenge

`$$ n $$`Unit

`$$ \mathrm{mol} $$`

The amount of substance \(n\) is the ratio between the number of particles \(N\) and the Avogardo constant \(N_{\text A} = 6 \cdot 10^{23}\):

`$$ n = \frac{N}{N_{\text A}} $$`So in one mole of gas there are \(6 \cdot 10^{23}\) gas particles.

## Gas constant

`$$ R $$`Unit

`$$ \frac{ \mathrm{J} }{ \mathrm{mol} \, \mathrm{K} } $$`

Gas constant is a physical constant appearing in thermodynamics. It has the following value:

`$$ R ~=~ 8.314 \, \frac{ \mathrm{J} }{ \mathrm{K} \, \mathrm{mol} } $$`