An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 6.3, Problem 31P
To determine
The average energy of a system is
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
If a particle of mass m moves with velocity v = (dr/dt) in the field, show that if E is constant the total energy of the particle E is given by E = (1/2)m (dr/dt)^2 + (1/5)kr^3 Make a rough sketch to describe this field.
Consider a classical of freedom" that is linear rather than quadratic: E = clql for some constant c. (An example would be the kinetic energy of a highly relativistic particle in one dimension, written in terms of its momentum.) Repeat the derivation of the equipartition theorem for this system, and show that the average energy is E= kT.
Consider a non-relativistic particle moving in a potential U(r).
Can either the phase or the group velocity of the particle exceed the speed
of light? What happens to the phase velocity vp at the turning point in
the potential U(x), where the particle gets reflected and the group velocity
vanishes, v - 0?
Chapter 6 Solutions
An Introduction to Thermal Physics
Ch. 6.1 - Prob. 2PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.1 - Prob. 6PCh. 6.1 - Prob. 7PCh. 6.1 - Prob. 8PCh. 6.1 - Prob. 9PCh. 6.1 - Prob. 10PCh. 6.1 - Prob. 11PCh. 6.1 - Prob. 12P
Ch. 6.1 - Prob. 13PCh. 6.1 - Prob. 14PCh. 6.2 - Prob. 15PCh. 6.2 - Prob. 16PCh. 6.2 - Prob. 17PCh. 6.2 - Prob. 18PCh. 6.2 - Prob. 19PCh. 6.2 - Prob. 20PCh. 6.2 - For an O2 molecule the constant is approximately...Ch. 6.2 - The analysis of this section applies also to...Ch. 6.3 - Prob. 31PCh. 6.4 - Calculate the most probable speed, average speed,...Ch. 6.4 - Prob. 35PCh. 6.4 - Prob. 36PCh. 6.4 - Prob. 37PCh. 6.4 - Prob. 39PCh. 6.4 - Prob. 40PCh. 6.5 - Prob. 42PCh. 6.5 - Some advanced textbooks define entropy by the...Ch. 6.6 - Prob. 44PCh. 6.7 - Prob. 45PCh. 6.7 - Equations 6.92 and 6.93 for the entropy and...Ch. 6.7 - Prob. 47PCh. 6.7 - For a diatomic gas near room temperature, the...Ch. 6.7 - Prob. 49PCh. 6.7 - Prob. 50PCh. 6.7 - Prob. 51PCh. 6.7 - Prob. 52PCh. 6.7 - Prob. 53P
Knowledge Booster
Similar questions
- Show that (x,t)=Aei(kwt) is a valid solution to Schrödinger's time-dependent equation.arrow_forwardThe basic problem of classical mechanics is simply stated : given a force law F(r,v,t)-a force F that may vary with position, velocity, and time- and initial conditions for positions and velocities, find the acceleration a = F/m and, from the acceleration, determine the trajectory r(t) for the particle. This procedure can be solved analytically in some cases; you can then derive an equation for position as a function of time. Let us state the step-by-step method in following words. 1. Start at the initial point with the initial velocity.2. Choose a time step ∆t.3. Calculate the force F and from it the acceleration a.4. Calculate the change in velocity ∆v = a∆t and the change in position ∆r = v∆t.5. The new velocity and position are then v + ∆v and r + ∆r, at the new time t+ ∆t.6. Since you are now at the next point on the particle trajectory, return to step 3 and repeat 3, 4, and 5 (as often as you wish). Acording to above lines calculate acceleration and velocity with time t until…arrow_forwardConsider a self-gravitating collection of particles. In such a situation, the mean kinetic energy of the particles will be 1/2 mv^2 = GM | 2R. This is approximate, and arises from something called the virial theorem that you will learn in upper level undergraduate classical mechanics. From this information, figure out what fraction of particles will be above the escape velocity from the collection of particles. (This calculation is relevant for understanding why star clusters evaporate over time).arrow_forward
- Compute the threshold energy needed for the physical process e+e− →µ+µ−. This is best computed in the center-of-momentum frame. Also describe how one could go from a lab frame where, for example, the stationary electrons interact with moving positrons to the center-of-momentum frame.arrow_forwardA Σ+ particle has a mean lifetime of 80.2 ps. A physicist measures that mean lifetime to be 403 ps as the particle moves in his lab. The rest mass of the particle is 2.12 x 10-27 kg. (a) How fast is the particle moving? (b) How far does it travel, as measured in the lab frame, over one mean lifetime? (c) What are its rest, kinetic, and total energies in the lab frame of reference? (d) What are its rest, kinetic, and total energies in the particle’s frame?arrow_forward(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 atarrow_forward
- Problem 3: A mass m is thrown from the origin att = 0 with initial three-momentum po in the y direction. If it is subject to a constant force F, in the x direction, find its velocity v as a function of t, and by integrating v find its trajectory. Check that in the non-relativistic limit the trajectory is the expected parabola. Hint: The relationship F = P is still true in relativistic mechanics, but now p = ymv instead of p = mv. To find the non-relativistic limit, treat c as a very large quantity and use the Taylor approximation (1+ x)" = 1 + nx when a is small.arrow_forwardAlbert Einstein is pondering how to write his (soonto-be-famous) equation. He knows that energy E is a function of mass m and the speed of light c, but he doesn't know the functional relationship (E = m2c? E = mc4?). Pretend that Albert knows nothing about dimensional analysis, but since you are taking a fluid mechanics class, you help Albert come up with his equation. Use the step-by-step method of repeating variables to generate a dimensionless relationship between these parameters, showing all of your work. Compare this to Einstein's famous equation—does dimensional analysis give you the correct form of the equation?arrow_forwardCalculate the range of speeds for a particle of mass m in which the classical relation for the kinetic energy, (1/2)*m*v^2, is within 0.5 percent of the correct relativistic value. Find the values for an electron and a proton.arrow_forward
- Consider an observer at rest in a frame where the ambient air is also at rest. Far away to the left, a speaker emits sound waves at angular frequency ω0; far away to the right, an identical speaker (emitting the same frequency waves in its rest frame) is moving at velocity u to the right. Let v denote the speed of sound in air. A: Assuming the amplitude of waves from each speaker is the same, we might expect that the (complex) amplitude of sound waves is given by (for all points x between the two speakers)u(x, t) = A(e^(ik(x−vt)) + e^(ik'(x+vt))). (1)Here A is an unimportant overall constant prefactor. Use the Doppler effect (if needed), and otherphysics of waves, to determine k and k'in terms of u, v and/or ω.B: If the observer is at x = 0, the amplitude of oscillations is given by u(0, t). Show that if u << v, thenRe[u(0, t)] = 2A cos(ω1t) cos(ω2t) (2)where |ω2| << |ω1|. Find explicit formulas for ω1,2 in terms of ω0, u, v. cos(ω2t) varies extremely slowly in time. This…arrow_forwardConsider the motion of a particle in two dimensions given by the Lagrangian m L = 2 (x+ where i>0 . The initial conditions are given as y(0)=0, x(0) = 42 meters, *(0) = y (0) = 0. What is the value of x(t)– y(t) at t= 25 seconds in meters?arrow_forward5.3 A spaceship moves with speed V relative to an observer O, on a straight line which passes very near the observer. A source on the spaceship emits light of wavelength 2o = 500 nm in the frame of reference of the spaceship. For what range of the spaceship's speed will the light be visible to the observer? The wavelengths of visible light stretches from 2A = 400 nm to ig = 700 nm, approximately. Ans.: -0.22 < Bß<0.33arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax