# Difference between revisions of "Ideal gas: Energy"

Carl McBride (talk | contribs) m (Added R to equation.) |
(Expression for more degrees of freedom) |
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where <math>R</math> is the [[molar gas constant]]. | where <math>R</math> is the [[molar gas constant]]. | ||

− | 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. | + | 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. This result is valid only for a monoatomic ideal gas. The general expression would be |

+ | :<math>E = \frac{n}{2} NkT = \frac{n}{2} RT, </math> | ||

+ | where <math>n</math> is the number of degrees of freedom. This number is 3 for atoms; if would be 6 in principle for diatomic molecules, but in normal conditions 5 is a very good approximation since vibrations are "frozen" (as explained in the entry about [[degree of freedom | degrees of freedom]].) | ||

+ | |||

+ | |||

==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]] |

## Latest revision as of 16:44, 12 December 2008

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

where is the molar gas constant.
This energy is all *kinetic energy*, per degree of freedom, by equipartition. This is because there are no intermolecular forces, thus no potential energy. This result is valid only for a monoatomic ideal gas. The general expression would be

where is the number of degrees of freedom. This number is 3 for atoms; if would be 6 in principle for diatomic molecules, but in normal conditions 5 is a very good approximation since vibrations are "frozen" (as explained in the entry about degrees of freedom.)

## References[edit]

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