# What is Number of particles: Definition and 25 Discussions

The particle number (or number of particles) of a thermodynamic system, conventionally indicated with the letter N, is the number of constituent particles in that system. The particle number is a fundamental parameter in thermodynamics which is conjugate to the chemical potential. Unlike most physical quantities, particle number is a dimensionless quantity. It is an extensive parameter, as it is directly proportional to the size of the system under consideration, and thus meaningful only for closed systems.
A constituent particle is one that cannot be broken into smaller pieces at the scale of energy k·T involved in the process (where k is the Boltzmann constant and T is the temperature). For example, for a thermodynamic system consisting of a piston containing water vapour, the particle number is the number of water molecules in the system. The meaning of constituent particle, and thereby of particle number, is thus temperature-dependent.

In Particals consist (Ions, molecules, electrons, atom, compound etc.)

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1. ### A How does the number of particles increase the surface adsorption?

How the number of the particles in a solution increase the probability to get adsorption on a surface? which physical terms explain this? For example when I increase the concentration of molecules in a solution I can see that the adsorption and the aggregation on the surface happen.
2. ### I Why in BEC we must separate number of particles of ground state?

In BEC, why do we separate the number of particles of ground state(E=0) from the integral(total number of particles) when temperature below critical temperature. Why is the overall integral wrong while the index of sum of number of particle can be considered as continuous? Is it correct that...
3. ### I What is the relation between chemical potential and the number of particles?

Chemical potential is defined as the change in energy due to change in the number of particles in a system. Let we have a system which is defined by the following Hamiltonian: $$H = -t \sum_i^L c_i^\dagger c_{i+1} + V\sum_i^L n_i n_{i+1} -\mu \sum_i^L n_i$$ where ##c^\dagger (c)## are creation...
4. ### A How to choose the number of particles per site in Fermionic DMRG?

I am doing DMRG (in traditional formalism, not MPS) for Hubbard model H = -t ∑i ∑σci,σ ci+1,σ + U∑ini,σni,σ- In every iteration we add two sites to the system, but how do we set that how many particles are allowed in the system?
5. ### Is it correct to calculate the number of particles

I want to calculate that how many particles will be recorded by detector with MCNP. using the F8 tally which would provide energy spectrum, add all of data that related with full energy peak of spectrum, multiply by number of nps, then obtain the number of particles. is it correct ? i am not...
6. ### Entropy change when the number of particles decreases

Hi. I found following exercise in a high school textbook: "Compute the entropy change in following process:" The solution is "The number of particles decreases from ##N_1## to ##N_2=N_1/2##. Hence the entropy decreases by $$\Delta S=-k\cdot N_1\cdot \ln{2}\enspace ."$$ I can't quite follow...
7. ### I Fermi distribution interpretation

Hello! Let E_1, E_2, \ldots, E_n be n allowed energy levels for a system of electrons. This system can be described by the Fermi-Dirac distribution f(E). Each of those levels can be occupied by two electrons if they have opposite spins. Suppose that E_1, E_2, \ldots, E_n are such that...
8. ### I Differential number of particles in Fermi gas model

I'm practicing for the Physics GRE, and came across a question that has me stumped. "In elementary nuclear physics, we learn about the Fermi gas model of the nucleus. The Fermi energy for normal nuclear density (ρ0) is 38.4 MeV. Suppose that the nucleus is compressed, for example in a heavy ion...
9. ### I Energy of a number of particles

Hello! It is sometimes useful to find the average energy of a certain number N of particles contained in a box of volume V. In order to find this quantity, the total energy is required and then divided by N. The result is E_{average} = \displaystyle \frac{1}{N} \sum_{n = 1}^{N} \left| a_n...
10. ### Determine the number of particles transmitted by S-G analyzer

Homework Statement A beam of identical neutral particles with spin 1/2 travels along the y-axis. The beam passes through a series of two Stern-Gerlach spin analyzing magnets, each of which is designed to analyze the spin projection along the z-axis. The first Stern-Gerlach analyzer only allows...
11. ### Number of particles in the universe

I have a question that I didn't see covered in any book that I read in QFT (I read so far Srednicki which I finished and Peskin and Schroeder which I haven't finished), can the vacuum generate an infinite number of real particles? How do we generate real particles from virtual particles? Is...
12. ### Diffraction pattern for large number of particles

Why does a large number of identical particles randomly distributed produce a diffraction pattern same as that of a single particle?
13. ### Number of Particles in Universe: Protons, Neutrons, Electrons

Dear PF Forum, I'm just curious about these things. From what I read, the number of atoms in the universe is 1080 Hydrogen atoms. And neutrino is a billion times more. 1.2 x 1089 But what it said is actually the number of protons + neutrons, right? And about this. Is the number of protons and...
14. ### Avogadro's constant, number of moles, number of particles

Dealing with these has reminded me why I hated chemistry. What is the relationship between the above 3? Given atomic weight of nitrogen and Avogadro's constant, can the number of moles be found?
15. ### Chemical potential and fixed number of particles

Can we talk about the chemical potential of a system with fixed number of particles? Is this physically meaningful? Why/why not? P.s: I know that chemical potential is the partial derivative of free energy with respect to number of particles. But in the formulation of grand canonical...
16. ### Statistical Physics number of particles with spin 1/2 in a B-field

Homework Statement Homework Equations The Attempt at a Solution To be honest I'm clueless. I've missed a large amount of the course and just struggling to find any sources that explain this. I don't want the answer to the question, I want to figure that out for myself. What I really need is...
17. ### Question about the number of particles in the standard model.

Hi, I was just wondering why there are a finite number of fundamental particles in the universe. Why is it that when cern collide particles, the same particles are formed every time. Its like putting a hammer to a concrete block and every time you do so, the same chips with the same shape and...
18. ### Fock spaces semantics and number of particles

I was not formally introduced to this math, so I appreciate corrections but I'll give my impressions. The fock space for a particle with space H is (c, H, HxH, HxHxH, ... ) 1: What is a hilbert space for a single particle? I believe know what a hilbert space is, but for 'a particle'...
19. ### Calculating the number of particles colliding with an area per unit time

Homework Statement Consider a small portion (area=A) of the inside wall of a container full of gas. Show that the number of molecules colliding with this surface in a time interval Δt is PAΔt/(2mvx avg), where P is the pressure, m is the average molecular mass, and vx avg is the average x...
20. ### Number of Particles: Ne vs O - Is it the Same?

Homework Statement Do 5 L of Ne contain the same number of particles contained in 5 L of O ? 2. The attempt at a solution The book say yes but I know that 5 L of Neon are 4.5 g and 5 L of Oxygen are 7.15 g. So dividing them for their molecular weight I obtain 0.22 u and 0.44 u that aren't...
21. ### Volume over Number of Particles.

Homework Statement Just a general inquiry. Homework Equations The Attempt at a Solution This there any physical significance to this ratio?
22. ### Boltzmann statistics - finding the number of particles

Boltzmann statistics -- finding the number of particles Homework Statement A column of water contains fine spherical metal particles of radius 2 x10-8m, which are in thermal equilibrium at 25C. If there are 1000 particles per unit volume at a given height, how many particles would be found...
23. ### Calculating the Number of Particles in Your Room

The EPA has proposed a new standard for microparticulates in air: for particles up to 2.5 µm in diameter, the maximum allowable amountin 50 µg/m^3. If your 9.3 ft x 9.25 ft x 11.3 ft dorm room just meets the new EPA standard, how many of these particles are in your room? How many of these...
24. ### Finding total number of particles in a given distribution

Homework Statement N particles are distributed amongst three levels having energies 0, kT, 2kT. If the total equilibrium energy of the system is approximately 425kT, what is the value of N?Homework Equations Probability of finding a particle at an energy level is: P_n = Aexp\left({-\epsilon_n...
25. ### System with big number of particles

System with "big" number of particles.. Let's suppose we have a Hamiltonian of the form: H(q_1 ,q_2 ,q_3,..., q_N , p_1,p_2 ,p_3 , ..., p_N ) \Phi (q_1 ,q_2 ,q_3,..., q_N) = E_{n} \Phi (q_1 ,q_2 ,q_3,..., q_N ) but the problem is that N is very "big" , let's say N \rightarrow \infty ...