(a) Derive an expression for the variance in the number of particles in a state for a Bose-Einstein gas when the number of particles in the gas can change.(b) Using the particle number for the Bose-Einstein gas, determine any specific properties ofthe chemical potential.

This question is complex , hence i am solving only first part , please post second part again . (a)…

Answered: (a) Derive an expression for the…

(a) Derive an expression for the variance in the number of particles Einstein gas when the number of particles in the gas can change.

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter10: Statistical Physics

Section: Chapter Questions

Problem 1Q

See similar textbooks

Related questions

Q: The average translational kinetic energy for a molecule (Errans) is given by the following equation:…

A: The average velocity at T = 200 C is given as v2=3kTmv12=3k200mv12=600km Now the kinetic energy at T…

Q: 12.4 (a) What is the average density of the sun? (b) What is the av- erage density of a neutron star…

A: Density = D = m / V In case of the neutron star we know that it has the same mass as the sun, m =…

Q: The average kinetic energy of a gas molecule at 100°C is:

Q: Discuss what is required to be true for the molar-averaged and mass-averaged velocities to be…

Q: A modern-day zeppelin holds 8,410 m3 of helium. Compute its maximum payload at sea level. (Assume…

Q: In this problem we will deal with simple thermodynamics model of a black hole. Assume that the…

Q: 10000 1000- co, solid 100 co, liqud Sublim aton point -785°C at 1 atm 10- 0.1- 001- co, gas 0001…

Q: Evaluate the statement whether it is true or false: The temperatures of the liquids were measured in…

Q: What is the mass of air at 20 degrees Celcius in a room with dimensions 3m by 4m by 5m?

A: Given data: The dimensions of the room are 3 m×4 m×5 m. The density of air, ρair=1.20 kg/m3.…

Q: What is the physical significance of the universal gas constant R?

A: The gas constant is, by convention, symbolized R. The gas constant is also well-known as the molar,…

Q: 12.4 • (a) What is the average density of the sun? (b) What is the av- erage density of a neutron…

A: We have given condition that if the radius of the neutron star is 84.66 km? Then what is the the…

Q: At atmospheric pressure and a temperature of 3.64 K helium can still exist in gas phase. Find the…

Q: A galss flask of volume 461 cm3 is totally filled with a mercury at 66 °C. When the temprature of…

Q: 12.4• (a) What is the average density of the sun? (b) What is the av- erage density of a neutron…

Q: What is the estimated VOLUME expansion coefficient, B f.

Q: A worker pressurized a rigid pipe (with an inside diameter of 30 mm and length of 20 m) with dry air…

A: The volume of the pipe is, V=π4d2L=π430 mm0.001 m1 mm220 m=π40.03 m220 m=0.01413 m3 The initial and…

Q: At maximum speed, a kinesin molecule moves at a rate of 6400 Å per second. Given the dimensions of…

A: It is given that R=6400 A/sD=80 AL=10 feet

Q: Water is poured into a container that has a leak. The mass m of the water is given as a function of…

A: Given: The function of mass is,

Q: 27. The Carnot Theorem states that,

A: Carnot gives the theorem of Thermodynamics to explain the efficient engine.

Q: prove average total kinetic energy = 2kT for gas molecules crossing a spherical area, with the…

A: At normal temperature the molecules are randomly moving in an ideal gas. The velocities of the…

Q: Derive the perfect gas equation.

A: write the expression for the boyle's law, charles law and avogadro's law,

Q: The pressure gauge on a cylinder of gas registers the gauge pressure, which is the difference…

Q: 5. (Ch. 19- Exercise 23 in Wolfson) For a gas of six molecules confined to a box, find the…

A: A box has total two sides, N= 2 (Left & Right) Total number of particles (n) = 6 (a) All the…

Q: The kinetic energy of gas molecules is zero at _______?

A: According to question we need to find--- The kinetic energy of gas molecules is zero at _______?

Q: By how much does the average kinetic energy of the center-of-mass motion of the molecules of a…

A: The average kinetic energy is

Q: Under what conditions is the ideal-gas assumption suitable for real gases?

Q: How real gases different from ideal gases?

A: Following are the ways to differentiate real gases from ideal gases: i) Real gases have inelastic…

Q: 2.9. (a) Solve the integral (dx1...dx3N) 3N and use it to determine the "volume" the relevant region…

Q: A car engine moves a piston with a circular cross sectionof 7.500 ± 0.002 cm diameter a distance…

Q: dP dq Prove That dT TdV With the equation of Clausius Calpeiron

Q: Consider the Universe to be spherical, mostly hydrogen gas molecules undergoing adiabatic expansion…

Q: Calculate the root mean square, average, and most probable velocities in centimeters per second of…

A: The rms velocity, average velocity and the most probable velocity for a gas at a given temperature…

Q: If the temperature of an ideal gas is held constant, the relationship between its pressure in…

Q: ap. ap) ; =?,, =?, av =? ƏT

A: We need to calculate certain partial derivatives in the van der Waals equation.

Q: Find the value of (), where(), = a/k and 9, = -Vk, Using Maxwell relation in thermodynamic.

Q: A modern-day zeppelin holds 7,620 m3 of helium. Compute its maximum payload at sea level. (Assume…

A: The expression for the net force,

Q: Show the complete solution that the coefficient of volume expansion can be expressed as in the…

A: Introduction: In calculating the entropy change for a solid under isothermal pressure change, we…

Q: Assume you are using the attached pressure gauge and a thermocouple with a temperature uncertainty…

Q: Is the total energy of the universe is constant? How?

A: According to the conservation of energy, the total energy of the universe is constant. Energy can…

Q: The average kinetic energy of a gas molecule at 100 °C is:

A: Temperature (T) = 100° C or T = 273+100 = 373 K

Q: In ideal gas, what happens to the pressure and temperature if the conainter of gas particles becomes…

A: for ideal gas; P α 1V Boyle's lawandV α T Charles's Law

Question

100%

(a) Derive an expression for the variance in the number of particles in a state for a Bose-
Einstein gas when the number of particles in the gas can change.
(b) Using the particle number for the Bose-Einstein gas, determine any specific properties of
the chemical potential.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1 Mean

Step 2 Variance

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 11 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

here R jl and nl is a function of x or k ??? i m confusd advance physics questionn
When two galaxies collide, the stars do not generally run into eachother, but the gas clouds do collide, triggeering a burst of new star formation. a) Estimate the probability that our Sun would collide with another star in the Andromeda galaxy if a collision between the Milky Way and Andromeda occured. Assume that each galaxy has 100 billion stars exactly like the sun, spread evenly over a circular disk with a radius of 100,000 lightyears. (Hint: first calculate total area of 100 billion circles with the radius of the Sun and then compare that to total area to the area of the Galatic disk) b) Estimate the probability of a collision between a gas cloud in our galaxy and one in the Andromeda galaxy. Assume that each galaxy has 100,000 clouds of warm hydrogen gas, each with a radius of 300 lightyears, spread evenly over the same disk. Use the same method as part A.
The energy dependence of the density of states for a two dimensional non-relativistic electron gas is given by, g(E)= CE" , where C is constant. The value of n is
(b) How do you find the expression for the total number of different and distinguishable ways in which n number of particles can be distributed among the various energy levels in the case of Bose-Einstein distribution law? How it differs from the Maxwell- Boltzmann and Fermi-Dirac distribution laws? Justify the reasons of those differences.
Calculate the following quantities for a three-dimensional classical ideal gas: (a) (vx), (b) (v?). (c) (v*vx), (d) (vàvy), (e) ((Vx + () (v²v?). bv,)^) (b a constant),
Check Your Understanding For the particle in the example, find the probability Of locating it 0 and L/4.
Check Your Understanding If a=3+4i , what is the product a* a?
Assume that an atomic nucleus can be thought of as a three-dimensional box with a width of 2 x 10^-14 m. If a proton moving as particles in this box, specify : Energy is excited first and second.
The degeneracy pressure of the electrons can stabilize the collapse of a star due to gravity by equating the gravitational inward pressure with the outward electron gas degeneracy pressure. These cold stars called white dwarfs have small radii compared to their original size and this radius decreases as the original mass of the star increases. As the mass of a star increases, the electron energy increases to a point in which their energy has to be treated relativistically. (a) Evaluate the degeneracy pressure for ultra-relativistic electrons (problem 2, above). (b) As the pressure increases, the reaction e − + p → n + ν takes place. The neutrinos (ν) escape as matter is transparent to them, electrons and protons convert to neutrons until we are left with a neutron star. Using your expression for the degeneracy pressure obtained in (a) above, equate the gravitational pressureto the neutron degeneracy pressure (replace the electron’s mass in your degeneracy pressure expression from (a)…
This question is for modern physics and wave and particle: (a) To how small a region must an electron be confined for borderline relativistic speeds – say, 0.05c – to become reasonably likely? (Ans: 3.9×10^−12m ) (b) On the basis of this, would you expect relativistic effects to be prominent for hydrogen’s electron, which has an orbit radius near 10-10? For a lead atom “inner-shell” electron of orbit radius 10-12m?
When the temperature of a mole of boson gas is half its critical temperature for Bose-Einstein condensation, its specific heat (in terms of R) is:
A hole is the absence of an electron at a potential location for its existence. Given that a hole is the result of the absence of an electron, its mass should be zero. However, we regard the effective mass of a hole to be negative. Why?