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.
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...
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...
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...
Homework Statement
What is the average energy of the CMB photons, in electronvolts, for ##T=2.73K##?
Homework EquationsThe Attempt at a Solution
I used the grand canonical ensemble for photons and after several calculations I get $$<E>=\frac{8\pi V}{c^3}\int_0^\infty \frac{h\nu^3}{e^{\beta h...
Homework Statement
Homework Equations
Q(t) = Aei(wt+Φ); dQ/dt = i*w*Q(t); E = (L/2)(dQ/dt)2 + Q2/2C
i = √-1 E above is average energy
The Attempt at a Solution
When I plug in Q(t) & dQ/dt into equation above (E) I get:
A2L/2(w02-w2)cos[2(wt+Φ)]
w02 = 1/LC
After I plugged both of them in...
Homework Statement
Given a wave function that is the super position of the two lowest energies of a particle in an infinite square well ##\Psi = \frac{\sqrt{2}}{\sqrt{3}}\psi _1 + \frac{1}{\sqrt{3}}\psi _2##, find ##\langle E \rangle##.
Homework EquationsThe Attempt at a Solution
I'm not sure...
Homework Statement
http://imgur.com/a/lv6Uo
Homework Equations
Look below
The Attempt at a Solution
I was unsure where to start. I thought that parseval's theorem may be helpful. I know the Potential energy is equivalent to .5kx^2 and T will be the integral of the force. So i have $$<E> =...
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...
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.
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...
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...
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...
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)...
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...
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...
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?
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}...
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...
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...
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...
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...
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...
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 ?
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...
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...
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...
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...
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...
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=...
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...
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...
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...
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...
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...