Equipartition Theorem Calculator
Equipartition Theorem Calculator computes energy per degree of freedom for systems at T, N, using relations like (∂T/∂V)_S.
Equipartition Theorem Overview
The equipartition theorem assigns \\(\frac{1}{2} k T\\) energy per degree of freedom:
\\[
\langle E \rangle = \frac{f}{2} N k T
\\]
Key properties:
- Total energy: \\(\langle E \rangle = \frac{f}{2} N k T\\)
- For ideal gas: \\( P = \frac{N k T}{V} \\)
Maxwell relation for internal energy (\\(U\\)):
\\[ \left( \frac{\partial T}{\partial V} \right)_S = -\left( \frac{\partial P}{\partial S} \right)_V \\]For ideal gas: \\( \left( \frac{\partial P}{\partial T} \right)_V = \frac{N k}{V} \\)
Example Calculation
Example: Ideal Gas with \\(T = 298 \, \text{K}, N = 6.022 \times 10^{23}, f = 3\\)
Differential: \\( dU = T dS – P dV \\)
Maxwell Relation: \\(\left( \frac{\partial T}{\partial V} \right)_S = -\left( \frac{\partial P}{\partial S} \right)_V\\)
Energy: \\(\langle E \rangle \approx 3.71 \, \text{kJ}\\)