By Keith Stowe
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Extra resources for Introduction To Thermodynamics And Statistical Mechanics
Suppose that P, is the probability that a system is in state s, c is a constant; and f and g are two functions that have the values S, and g,, respectively, when Lhe syslem is in stale s. 1 pruve Ilal: (a) (f =7+% (b) 7 = c f . 2. A coin is flipped many times. , the average value off per flip)? = 27, what is the mean 3. Thc numbcr of dots showing on a dic is n, and f (n) is somc function of n. If you were to roll many many dice, what would be the mean value off for (a) f = (n 212, @) f = (n - 2)2, (c) f = n Z - 5 n f 1, (d) f = n3 lo?
Find the probability that (a) exactly four molecules are in the front third and exactly six in the top half, (b) exactly three molecules are both in the front third and the top half (that is, the same molecules satisfy both criteria). 3 1. You roll two dice many times and are interested in the average value of the product of the two numbers showing, nln2. Calculate this product for all 36 possible different configurations of the two dice and take the average of these 36 values. 8? Statistics for small systems 32.
In its x-component of velocity'? 14. Consider a particle moving in one dimension. , the velocity is between +lo7 and -107 d s ) . 15. Consider a proton moving in three dimensions, whose motion is confined to be within a nucleus (a sphere of radius 2 x 10-l5 m) and whose momentum must have magnitude less than po = 3 x 10-l9 kgmls. Roughly how many Introduction to thermodynamics and statistical mechanics quantum states are available to this proton? ) 16. A particle is confined within a rectangular box with dimensions 1 cm by 1 cm by 2 cm.