Ideal gas: Energy: Difference between revisions

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


:<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 \equiv \frac{3}{2} RT </math>


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.
==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 14:33, 4 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.

References

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