An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Question
Chapter 3.2, Problem 15P
To determine
The heat capacity of a star using virial theorem.
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Show that if A and B are matrices which don’t commute, then eA+B = eAeB, but if they do commute then the relation holds. Hint: Write out several terms of the infinite series for eA, eB, and eA+B and do the multiplications carefully assuming that A and B don’t commute. Then see what happens if they do commute.
I have been able to do this with derivatives but I can't figure out how to do this with definite integrals
write the solution step by step and clearly.
Chapter 3 Solutions
An Introduction to Thermal Physics
Ch. 3.1 - Use Table 3.1 to compute the temperature of solid...Ch. 3.1 - Use the definition of temperature to prove the...Ch. 3.1 - Figure 3.3 shows graphs of entropy vs. energy for...Ch. 3.1 - Can a miserly system, with a concave-up...Ch. 3.1 - Prob. 5PCh. 3.1 - Prob. 6PCh. 3.1 - Prob. 7PCh. 3.2 - Prob. 8PCh. 3.2 - In solid carbon monoxide, each CO molecule has two...Ch. 3.2 - An ice cube (mass 30 g) at 0C is left sitting on...
Ch. 3.2 - In order to take a nice warm bath, you mix 50...Ch. 3.2 - Estimate the change in the entropy of the universe...Ch. 3.2 - When the sun is high in the sky, it delivers...Ch. 3.2 - Experimental measurements of the heat capacity of...Ch. 3.2 - Prob. 15PCh. 3.2 - A bit of computer memory is some physical object...Ch. 3.3 - Prob. 17PCh. 3.3 - Prob. 18PCh. 3.3 - Prob. 19PCh. 3.3 - Prob. 20PCh. 3.3 - Prob. 21PCh. 3.3 - Prob. 22PCh. 3.3 - Prob. 23PCh. 3.3 - Prob. 24PCh. 3.3 - Prob. 25PCh. 3.3 - Prob. 26PCh. 3.4 - What partial-derivative relation can you derive...Ch. 3.4 - A liter of air, initially at room temperature and...Ch. 3.4 - Sketch a qualitatively accurate graph of the...Ch. 3.4 - As shown in Figure 1.14, the heat capacity of...Ch. 3.4 - Experimental measurements of heat capacities are...Ch. 3.4 - A cylinder contains one liter of air at room...Ch. 3.4 - Prob. 33PCh. 3.4 - Polymers, like rubber, are made of very long...Ch. 3.5 - Prob. 35PCh. 3.5 - Prob. 36PCh. 3.5 - Prob. 37PCh. 3.5 - Suppose you have a mixture of gases (such as air,...Ch. 3.6 - Prob. 39P
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- Consider the van der Waals potential U(r)=U0[( R 0 r)122( R 0 r)6] , used to model the potential energy function of two molecules, where the minimum potential is at r=R0 . Find the force as a function of r. Consider a small displacement R=R0+r and use the binomial theorem: (1+x)n=1+nx+n( n1)2!x2+n( n1)( n2)3!x3+ , to show that the force does approximate a Hooke’s law force.arrow_forwardPlease include detailed steps...especially in the integration part (u-sub)...arrow_forwardshow full work equationarrow_forward
- Use the tools for manipulating partial derivatives to prove the following relationsarrow_forwardA (nonconstant) harmonic function takes its maximum value and its minimum value on the boundary of any region (not at an interior point). Thus, for example, the electrostatic potential V in a region containing no free charge takes on its largest and smallest values on the boundary of the region; similarly, the temperature T of a body containing no sources of heat takes its largest and smallest values on the surface of the body. Prove this fact (for two-dimensional regions) as follows: Suppose that it is claimed that u(x, y) takes its maximum value at some interior point a; this means that, at all points of some small disk about a, the values of u(x, y) are nolarger than at a. Show by Problem 36 that such a claim leads to a contradiction (unless u = const.). Similarly prove that u(x, y) cannot take its minimum value at an interior point.arrow_forward
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