Download presentation

1
**The Heart of Statistical Mechanics**

Probability By: Jodi Schmelz

2
**Statistical Mechanics**

Key link between Quantum Mechanics and Thermodynamics Quantum Mechanics-microscopic level Thermodynamics-macroscopic level Statistical mechanics relates the microscopic and macroscopic properties through the Boltzmann equation Probability and statistics is the heart of statistical mechanics

3
**The Link The Boltzmann Equation is the link S=k ln W S is entropy**

k is Boltzmann’s constant W is the number of configurations of the ensemble

4
**Statistical Mechanics and Dice**

If two dice are rolled and there is no distinction between them the outcome is called a combination A permutation is when the two dice are distinct from one another is different from A microstate is one arrangement of the dice or one permutation A configuration is the collection of all equivalent microstates and is defined as “W”

5
Probability Probability (P): is a number between zero and one which tells the chance of a certain result or outcome occurring Probability is determined by the ratio of how many times an outcome can occur and how many possible outcomes there are.

6
Rolling Dice Let’s compare the probability of rolling a 2 to the probability of rolling a 7 There are 36 possible outcomes when two dice are rolled. There is only one way to roll a 2 P = 1/36 = 0.028 There are 6 possible ways to roll a 7 P = 6/36 = 0.167 (graph on next slide)

7
**The Odds of Rolling A Number With Fair Dice**

8
Loaded Die There is no longer an equal likelihood for each of the six outcomes One of the outcomes is favored more then the others A weight function is used to describe how each outcome is favored

9
**Loaded Die (cont.) Example of a Weight Function w(n) = 1/n**

If one die was being rolled the probability of rolling a 6 would be determined by: The probability of rolling a one would be:

10
Yes That’s Cheating When the loaded die is characterized by the weight function w(n)=1/n, the probability of rolling a 1 is six times greater than rolling a six. 0.408/0.068=6 Depending on how the dice is loaded the probability of rolling a specific number increases (Graph on next slide)

11
**Fair Dice vs. Loaded Dice**

12
References Dr. Darin J. Ulness. “Physical Chemistry 351 Notes.” (Concordia College, Moorhead, MN 2005) Dr. Darin J. Ulness. “Honors Chemistry 137 Notes.” (Concordia College, Moorhead, MN 2005) Statistics of Dice Throw at:

Similar presentations

Presentation is loading. Please wait....

OK

Boltzmann statistics, average values

Boltzmann statistics, average values

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on professional development Ppt on statistics in maths Presentation ppt on motivation and emotion How to do ppt on ipad Ppt on angle subtended by an arc of a circle Free ppt on different types of houses Ppt on 2nd world war Download ppt on reduce reuse recycle Ppt on power generation by speed breaker games Ppt on condition monitoring