Ideal gas: Energy: Difference between revisions
Jump to navigation
Jump to search
Carl McBride (talk | contribs) No edit summary |
(link added) |
||
| Line 3: | Line 3: | ||
:<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 13:46, 9 May 2008
The energy of the ideal gas is given by (Hill Eq. 4-16)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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}
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)