An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 6.3, Problem 31P
To determine
The average energy of a system is
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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
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vanishes, v - 0?
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.
The 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…
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
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