# What is average energy: Definition and 35 Discussions

In physics, a partition function describes the statistical properties of a system in thermodynamic equilibrium. Partition functions are functions of the thermodynamic state variables, such as the temperature and volume. Most of the aggregate thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives. The partition function is dimensionless.
Each partition function is constructed to represent a particular statistical ensemble (which, in turn, corresponds to a particular free energy). The most common statistical ensembles have named partition functions. The canonical partition function applies to a canonical ensemble, in which the system is allowed to exchange heat with the environment at fixed temperature, volume, and number of particles. The grand canonical partition function applies to a grand canonical ensemble, in which the system can exchange both heat and particles with the environment, at fixed temperature, volume, and chemical potential. Other types of partition functions can be defined for different circumstances; see partition function (mathematics) for generalizations. The partition function has many physical meanings, as discussed in Meaning and significance.

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1. ### I Average magnetic moment of atom in magnetic field ##B##

from the partition function - am trying to show that ##\langle \mu \rangle = \beta^{-1} (\partial \log Z / \partial B)## where ##Z## is the canonical partition function for one atom, i.e. ##Z = \sum_{m=-j}^{j} \mathrm{exp}(\mu_0 \beta B m)##, and ##\mu = \mu_0 m##. The average...
2. ### Confused about calculating the average energy from a distribution graph

Hello, in one of tasks of my liquid scintillation lab is to determine the average energy. You can see from the graph that data I obtained is similar to this one that I have a excel sheet data. X-axis is for beta particle energy from 0-156keV while y-axis counts of the particles. So according to...
3. ### Average Energy density and the Poynting vector of an EM wave

Hi, In Problem 9.12 of Griffiths Introduction to Electrodynamics, 4th edition (Problem 9.11 3rd edition), in the problem, he says that one can calculate the average energy density and Poynting vector as using the formula I don't really understand how to do...

8. ### Average energy for n-state system

Homework Statement Find the average energy ##\langle E \rangle## for (a) an n-state system in which a given state can have energy 0, ε, 2ε, 3ε... nε. (b) a harmonic oscillator, in which a state can have energy 0, ε, 2ε, 3ε... (i.e. with no upper limit). Homework Equations Definition of...
9. ### I Average energy of the electrons at T = 0

According to the quantum mechanical free electron model the average energy is E=3EF/5 for the 3D case. Nevertheless I saw in a specialised physics book that for the 1D model the average energy at T=0 is 0 and wanted to know if it is the same for the 3D case.
10. ### How Is the Average Energy Calculated in Statistical Mechanics?

Homework Statement If the energy of a system depends on ##E = \alpha |x|## where ##\alpha## is positive, what is the average energy of the system? Homework EquationsThe Attempt at a Solution I've been given no information at all about the system beyond the energy. This is within a statistical...
11. ### Average Energy Density of Capacitor

Homework Statement An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 48 mm and 72 mm. The electric potential of the inner conductor with respect to the outer conductor is -536 V (k = 1/4πε0 = 8.99 × 109 N · m2/C2) The average energy...
12. ### Average energy vs Energy of average

Hey, When performing Molecular dynamic or Monte Carlo simulation (in NPT or NVT ensemble), I'm wondering whether there is any difference between the average energy of the system and the energy of the average structure. If there is a difference, how munch should it be? and why? Does the the...
13. ### Ultra-relativistic gas average energy as E(T)

Homework Statement Ultra-relativistic particle with energy epsilon and momentum p is described by epsilon=cp. Find average energy E(T) of gas which consists of particles described above. Homework Equations So i think i should use this kind of equations(please use the link below)...
14. ### Calculating average energy of a system with 3 energy levels

Homework Statement A system has three energy levels, E1=0, E2 =1 and E3 = 2. In a certain state of the system, the probability that energy level 1 is occupied is 0.1, that energy level 2 is occupied is 0.8, and that energy level 3 is occupied is 0.1. Is this an equilibrium or a non-equilibrium...
15. ### Average energy mass on a spring

Homework Statement Hi, I hope this isn't a silly question. I am looking to find the mean potential energy of a mass on a spring with spring constant k and maximum displacement x0. Homework Equations The Attempt at a Solution I know the maximum energy is 1/2*kx0^2 so would the...
16. ### Deriving Average Energy Function For A Classical DOF

Hello everyone, The problem I am currently working is exactly what is given in this link: https://www.physicsforums.com/showthread.php?t=554243 However, I do not understand why we integrate between 0 and infinity. What is the motivation for doing so?
17. ### Average Energy and the Equipartition Theorem

The Equipartition Theorem states that each quadratic degree of freedom contributes 1/2 kT of energy. This can be derived for the translational degrees by integrating the average kinetic energy multiplied by the Maxwell velocity distribution: \int_{-\infty }^{\infty } \frac{m v^2}{2}...
18. ### Is there an analytical way to get average energy of a Fermi-Dirac gas?

The average particle energy of a Fermi-Dirac gas, with zero chemical potential, is about 3.15T, where T is the temperture of this gas. To get the average energy, one needs to do an integration. The integrand is something like \frac{x^3}{e^{x/k_BT}+1}. I could get the result numerically. But...
19. ### Statistical Physics - average energy of a system.

Homework Statement Imagine a system, in contact with a heat reservoir, with three particles. Each particle may be in a state of energy 0 or ε. What's the temperature of the reservoir such that the mean energy of the system, <E>, is 1.2ε? Homework Equations The Attempt at a...
20. ### Why isn't rotation included when calculating the average energy of a monatomic gas?

Greetings, this is my first post, though I have been reading these forums for a while. I understand that the average energy of each degree of freedom in a thermodynamic system in equilibrium is kT/2. My textbook says that for a monatomic gas particle, the only degrees of freedom that count...
21. ### Average Energy of Grand Canonical Ensemble

Hello, The entropy of the Grand Canonical Ensemble (GCE) is: S = KB ln ZG + (\bar{E}/T) - μo\bar{N}/T Helmholtz function is: F = \bar{E} - TS = \bar{E} - TKB ln ZG - \bar{E} + μo\bar{N} = -TKB ln ZG + μo\bar{N} But \partialF/\partialT = -S (From thermodynamics). Then...
22. ### Average energy density in a pulse of incoherent radiation

This is from Physics of Atoms and Molecules - Bransden, Joachain - Section 4.1 Homework Statement Show that the average energy density in a pulse of the form (4.13) is \overline{\rho}=2\int_{\Delta\omega}\omega^{2}A_{0}^{2}\left(\omega\right)\mathrm{d}\omega Homework Equations...
23. ### The average energy = the most probable energy?

Hi, Just like what the Title tells about. In the Statistical Physics, keeping the desity unchanged while taking the limit of Number(or Volume)=infinity. Does the average energy equal to the most probable energy ?
24. ### Photon Average Energy in a Cavity Resonator

The rms EM field within a cavity resonator, excited in a single resonant mode by a current probe of fixed rms amplitude, is known to rise linearly with time; eg. http://www.jpier.org/PIER/pier78/15.07090605.Wen.pdf", sections 5.2, 5.3, fig's. 6, 10. (Normally it is a fixed driving voltage...
25. ### How Does Oscillator Frequency Affect the Energy Ratio K/E?

Homework Statement Express the ratio of the average kinetic energy K to the average total energy E of the oscillator in terms of the dimensionless quantity ωo/ω. Homework Equations I found that: K = (1/2)mA^2ω^2 sin^2(ωt − δ) E = (1/2)mA^2[ω^2 sin^2(ωt − δ) + ωo^2 cos^2(ωt − δ)] The...
26. ### Average Energy of Boltzmann Distribution

The question is: Write an expression for the average energy of a set of particles obeying Boltz- mann statistics and each having energy E = bz2, where b is a constant and z is a variable. Hence, show that the average energy per degree of freedom for each particle is 1 2kBT; where kB is...
27. ### Finding the average energy density of an EM wave in a magnetic field

Hi, I've not posted on here before but I'm trying to keep on top of work over the summer and I'm having some real problems with this question Homework Statement Consider the plane polarised EM wave in a source free vacuum with magnetic field B = (1,1,0)B0cos(kz-wt) where B0 = 0.001T. Find...
28. ### Average energy of atoms in the Stern–Gerlach experiment

I have been reading about the Stern–Gerlach experiment and found that the atoms leaving the oven in the experiment have an average energy of 2kT, rather than an energy of 3kT/2 for a gas. I can not find a reason for this higher energy myself and would like suggestions on why this seems to be...
29. ### Average energy of a harmonic oscillator

Hello PF members, Is there some good book, which contain the derivation of average energy of a harmonic oscillator at temperature T. I want to derive from Planck's distribution (PD) function (<n>=(exp(##\hbar\omega/kT##)-1)##^{-1}##)...to get the following relation: energy E=...
30. S

### Proof of average energy of quantum oscillator

proove that the average energy of a quantum oscillator = hw/(e^(hw/kT)-1) where h= h bar w=omega k=boltzmann constant T=temp
31. ### Statistical mechanics average energy

Homework Statement average energy per particle u = (Eo + E1 e^(-B deltaE)) / (1 + e^(-B deltaE)) B = 1/T Homework Equations Possibly relevant: e^x = 1 + x^2 / 2! + x^3 / 3! ... The Attempt at a Solution It tells me the average energy is about u = Eo + (deltaE)e^(-B delatE) as...
32. ### How to Solve for Average Energy as T Approaches 0 and Infinity

I'm having some difficulties with a problem. Based on the constraints, I have found that the average energy per particle is u = (Eo + E1 e^(-B deltaE)) / (1 + e^(-B deltaE)). I know this is correct. However, I am having problems solving as T approaches 0 and infinity. B = 1/T It tells me the...
33. ### Planck average energy reduce to Boltzmann energy

Hi I'm new here with new problem. I have to show how can the Planck average energy reduce to Boltzmann energy in the limit of no quantization, but I have some problems to understand how should I solve this. If you have any ideas or answers or maybe some materials please send me a MAIL or...
34. ### Average energy of gas of fermions at T = 0

Consider a system of N (>>1) particles with mass m in a (big) volume V. What is the average energy per particle if the particles are fermions. I did some calculations and I came up with <E> = (2/3)*Fermi-energy. Is this correct? I could post my calculations but my Latech-skills are very...
35. ### Calculate Average Energy Use/Month

I'm helping a friend with this question and wanted to make sure I was doing it correctly... Suppose your local power company charges 6.3 cents per kilowatt hour and your most recent bill came to \$27.00. How much energy, on average, did you use (in Joules) per second last month? Assume that...