2.9. (a) Solve the integral (dx1...dx3N) 3N and use it to determine the "volume" the relevant region of the phase space of an extreme relativistic gas (8 = pc) of 3N particles moving in one dimension. Determine, as well, the number of ways of distributing a given energy E among this system of particles and show that, asymptotically, wo = h3N_ (b) Compare the thermodynamics of this system with that of the system considered in Problem 2.8.

2.9. (a) Solve the integral (dx1...dx3N) 3N and use it to determine the "volume" the relevant region of the phase space of an extreme relativistic gas (8 = pc) of 3N particles moving in one dimension. Determine, as well, the number of ways of distributing a given energy E among this system of particles and show that, asymptotically, wo = h3N_ (b) Compare the thermodynamics of this system with that of the system considered in Problem 2.8.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

(a) Let L be the diameter of our galaxy.Suppose that a person in a spaceship of massm wants to travel across the galaxy at constantspeed, taking proper time τ. Find the kineticenergy of the spaceship. (b) Your friend is impa-tient, and wants to make the voyage in an hour.For L = 105 light years, estimate the energy inunits of megatons of TNT (1 megaton=4×109 J).
4.3 Time dilation for a biological clock. I trim my moustache every 6 weeks. If I were in a rocket ship flying past you at a speed of V=c, then how much time, in your frame, would elapse between my moustache trimmings? 44 Munn lifetime. The lifetime of a stationary muon is 2.2 microseconds. A beam of
Your video analysis of the motion of a marble gives it position in frame 23 as (x23, Y23) = (0.134 m, 0.120 m) and its position in frame 24 as (x24, 324) = (0.122 m, 0.112 m). You esti- mate that you can measure the r and y positions with uncertainty +0.003 m. The frame rate of the video is 30 frames/s, which means the time interval between frames is At = 0.033 333 s. The uncertainty of the frame rate of a video camera is VERY small. For the sake of this prob- lem, use 8(At) = 1 x 10-6 s. The mass of the marble is (2.031 +0.001) x 10-2 kg. Calculate the following quantities: 4. The value of the momentum component p = mv, and its uncertainty, 5. The value of the momentum component py = muy and its uncertainty, and 6. The value of the kinetic energy K = mv² = m(v² + v²) and its uncertainty.
Needs Complete typed solution with 100 % accuracy.
The Tevatron was a large particle accelerator that would collide beams ofprotons and anti-protons to see what would come out of the collisions.a) Let’s assume that each particle (in both beams) was accelerated to a total energy of100 GeV. What is the speed of the protons (relative to the speed of light) if you assumethe mass of the proton is equal to 1 GeV/c^2? Write your answer in terms of the speed oflight—keep it as a decimal times “c”. You will need several decimal places.b) Suppose that you now accelerate each particle to a speed of 0.9c. Since they are movingin opposite directions, what is the speed that one would measure for the speed of the otherparticle? Just give the absolute value of this speed. Don’t worry about the sign.c) Given your answer in part b, what is the energy of that one particle would measure forthe other particle?
A particle is measured to be in the interval 0 < x < x0. According to the many-worlds interpretation, what is the best way to describe where the particle was immediately before the measurement was performed?
In a parallel universe, the quantity t has the value 3.14049... Express a in that universe to (a) four significant figures: (b) five significant figures:
I need help on Question 7!
Particle physicists use particle track detectors to deter- mine the lifetime of short-lived particles. A muon has a mean lifetime of 2.2 µs and makes a track 9.5 cm long before decaying into an electron and two neutri- nos. What was the speed of the muon?
(a) Find the momentum (in kg- m/s) of a 1.20 x 109 kg asteroid heading towards the Earth at 3,050 km/s. (Hint: Use the approximation that y = 1 + 2c² least six significant figures.) kg-m/s (b) Find the ratio of this momentum to the classical momentum. (Enter your answer to at least six significant figures.) Р Pclassical at low velocities. Enter your answer to at