×
Get Full Access to An Introduction To Thermal Physics - 1 Edition - Chapter 6 - Problem 51p
Get Full Access to An Introduction To Thermal Physics - 1 Edition - Chapter 6 - Problem 51p

×

# In this section we computed the single-particle

ISBN: 9780201380279 40

## Solution for problem 51P Chapter 6

An Introduction to Thermal Physics | 1st Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

An Introduction to Thermal Physics | 1st Edition

4 5 1 283 Reviews
18
2
Problem 51P Problem 51PIn this section we computed the single-particle translational partition function, Ztr by summing over all definite-energy wave functions. An alternative approach, however, is to sum over all possible position and momentum vectors, as we did in Section 2.5. Because position and momentum are continuous variables, the sums are really integrals, and we need to slip in a factor of 1/h3 to get a unitless number that actually counts the independent wave functions. Thus, we might guess the formulawhere the single integral sign actually represents six integrals, three over the position components (denoted d3r) and three over the momentum components (denoted d3p). The region of integration includes all momentum vectors, but only those position vectors that lie within a box of volume V. By evaluating the integrals explicitly, show that this expression yields the same result for the translational partition function as that obtained in the text. (The only time this formula would not be valid would be when the box is so small that we could not justify converting the sum in equation to an integral.)

Step-by-Step Solution:
Step 1 of 3

MATH 10B Lecture #10 Notes Ivan Lopez October 25 2016 End of Section 6.1: Line Integrals 3 De▯nition: A simple curve in the image (range) C of a map c : [a;b] ! R (or R ), which is 1-1 (one-to-one, which is to say that C(t ) =1 6 C(t 2 if t16= t2and does not have any self-intersections except possibly at endpoints). In addition, the curve is a simple closed curve if c(a) = c(b). Remark: A curve is called simple if it is both x-simply and y-simple. Let us now focus on how line integrals are independent of reparametrization. From the this image, we can make the following statements: We have a curve C, where we have c : [a

Step 2 of 3

Step 3 of 3

##### ISBN: 9780201380279

An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279. Since the solution to 51P from 6 chapter was answered, more than 279 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1. The full step-by-step solution to problem: 51P from chapter: 6 was answered by , our top Physics solution expert on 07/05/17, 04:29AM. This full solution covers the following key subjects: position, momentum, Integrals, vectors, section. This expansive textbook survival guide covers 10 chapters, and 454 solutions. The answer to “In this section we computed the single-particle translational partition function, Ztr by summing over all definite-energy wave functions. An alternative approach, however, is to sum over all possible position and momentum vectors, as we did in Section 2.5. Because position and momentum are continuous variables, the sums are really integrals, and we need to slip in a factor of 1/h3 to get a unitless number that actually counts the independent wave functions. Thus, we might guess the formula where the single integral sign actually represents six integrals, three over the position components (denoted d3r) and three over the momentum components (denoted d3p). The region of integration includes all momentum vectors, but only those position vectors that lie within a box of volume V. By evaluating the integrals explicitly, show that this expression yields the same result for the translational partition function as that obtained in the text. (The only time this formula would not be valid would be when the box is so small that we could not justify converting the sum in equation to an integral.)” is broken down into a number of easy to follow steps, and 177 words.

#### Related chapters

Unlock Textbook Solution