Ideal gas: Energy: Difference between revisions

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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 15:44, 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]

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