# Difference between revisions of "Ideal gas: Energy"

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:<math>E = -T^2 \left. \frac{\partial (A/T)}{\partial T} \right\vert_{V,N} = kT^2 \left. \frac{\partial \ln Q}{\partial T} \right\vert_{V,N}= NkT^2 \frac{d \ln T^{3/2}}{dT} = \frac{3}{2} NkT</math> | :<math>E = -T^2 \left. \frac{\partial (A/T)}{\partial T} \right\vert_{V,N} = kT^2 \left. \frac{\partial \ln Q}{\partial T} \right\vert_{V,N}= NkT^2 \frac{d \ln T^{3/2}}{dT} = \frac{3}{2} NkT</math> | ||

− | This energy is all ''kinetic energy'', <math>1/2 | + | This energy is all ''kinetic energy'', <math>1/2 kT</math> per [[degree of freedom]], by [[equipartition]]. This is because there are no intermolecular forces, thus no potential energy. |

==References== | ==References== | ||

#Terrell L. Hill "An Introduction to Statistical Thermodynamics" 2nd Ed. Dover (1962) | #Terrell L. Hill "An Introduction to Statistical Thermodynamics" 2nd Ed. Dover (1962) | ||

[[category: ideal gas]] | [[category: ideal gas]] |

## Revision as of 14:46, 9 May 2008

The energy of the ideal gas is given by (Hill Eq. 4-16)

This energy is all *kinetic energy*, per degree of freedom, by equipartition. This is because there are no intermolecular forces, thus no potential energy.

## References

- Terrell L. Hill "An Introduction to Statistical Thermodynamics" 2nd Ed. Dover (1962)