Editing Ideal gas: Energy
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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>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.kT</math> per degree of freedom. 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]] |