lec16_[EDocFind.com] - Thermo & Stat Mech -...

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Unformatted text preview: Thermo & Stat Mech - Spring 2006 Class 16 1 Thermodynamics and Statistical Mechanics Probabilities Thermo & Stat Mech - Spring 2006 Class 16 2 Pair of Dice For one die, the probability of any face coming up is the same, 1/6. Therefore, it is equally probable that any number from one to six will come up. For two dice, what is the probability that the total will come up 2, 3, 4, etc up to 12? Thermo & Stat Mech - Spring 2006 Class 16 3 Probability To calculate the probability of a particular outcome, count the number of all possible results. Then count the number that give the desired outcome. The probability of the desired outcome is equal to the number that gives the desired outcome divided by the total number of outcomes. Hence, 1/6 for one die. Thermo & Stat Mech - Spring 2006 Class 16 4 Pair of Dice List all possible outcomes (36) for a pair of dice. Total Combinations How Many 2 1+1 1 3 1+2, 2+1 2 4 1+3, 3+1, 2+2 3 5 1+4, 4+1, 2+3, 3+2 4 6 1+5, 5+1, 2+4, 4+2, 3+3 5 Thermo & Stat Mech - Spring 2006 Class 16 5 Pair of Dice Total Combinations How Many 7 1+6, 6+1, 2+5, 5+2, 3+4, 4+3 6 8 2+6, 6+2, 3+5, 5+3, 4+4 5 9 3+6, 6+3, 4+5, 5+4 4 10 4+6, 6+4, 5+5 3 11 5+6, 6+5 2 12 6+6 1 Sum = 36 Thermo & Stat Mech - Spring 2006 Class 16 6 Probabilities for Two Dice 2.8 5.6 8.3 11 14 17 14 11 8.3 5.6 2.8 % 36 1 36 2 36 3 36 4 36 5 36 6 36 5 36 4 36 3 36 2 36 1 Prob. 12 11 10 9 8 7 6 5 4 3 2 Total Thermo & Stat Mech - Spring 2006 Class 16 7 Probabilities for Two Dice Dice 0.05 0.1 0.15 0.2 2 3 4 5 6 7 8 9 10 11 12 Number Probability Thermo & Stat Mech - Spring 2006 Class 16 8 Microstates and Macrostates Each possible outcome is called a microstate....
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lec16_[EDocFind.com] - Thermo & Stat Mech -...

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