1 Boltzmann's Epitaph, an idea to die for!?! 2 At
Students also viewed these physics questions
At the beginning of 2009, the Healthy Life Food Company purchased equipment for $42 million to be...... ... in service life from 10 years to 5 years to me,” Dent concluded. “Let\'s go with it that way, Heather.”Required:1. What is the difference in before-tax income between the CEO\'s and...
View Answer
A stock that sold for $22 at the beginning of the year was selling for $24 at the end of the year. If the stock paid a dividend of $.50 per share, what is the simple interest rate on an investment in this stock?
View Answer
On January 11, at the beginning of your annual audit of the Grover Manufacturing Company’s...... ... in an attempt to:1. Discover evidence within the purchasing department of defalcations being committed by the buyer. Give the purpose of each audit procedure.2. Provide leads about possible...
View Answer
One Product Corp. (OPC) incorporated at the beginning of last year. The balances on its...... $... equal amounts over the next three years. If OPC can earn 7 percent interest compounded annually, how much cash would OPC need to invest equally at the end of each of the next three years to have saved...
View Answer
At the beginning of the current (non-leap) year, Charles owns all of Pearl Corporation’s...... ... Donald? What is Donald’s basis in his Pearl stock at the end of the year?a. Current E&P of $40,000; accumulated E&P of $30,000.b. Current E&P of $100,000; accumulated E&P (deficit) of ($50,000).c....
View Answer
Read the following case and calculate the book value of Home Depot\'s current and prior year fixed...... a... and kitchen equipment, among others. The following information is from the company\'s books. Fixed assets Current year last year Buildings $28,300 $21,500 Machinery, equipment and computer...
View Answer
What causes an entire row of zeros to show up in the Routh table?
View Answer
Not included in the table below is a diamond with a weight of 1.50 carats. Find the best predicted price for this diamond. Is the result close to the actual price of $16,097? What is wrong with predicting the price of a 1.50-carat diamond? Find the regression equation using α = 0.05, letting the...
View Answer
6) Using the airline\'s between-flight cost data given as follows, prepare a CPM/Cost analysis for each of the following three points in time, For each case, show the percent overrun or underrun for the project to date and indicate any corrective action that should be undertaken. MDIST AY2020/21Sem...
View Answer
Lok Sabha in India is to discuss a key constitutional amendment, and there will be four rounds of voting. In each round of voting, assume that the ruling party has a 60% chance of winning, i.e. getting the resolution passed by majority vote. Further assuming that the voting rounds are independent...
View Answer
The March 31, 2014, adjusted trial balance for sopik Refrigeration Repairs is shown below with...... (a) would not appear on the post closing trial balance.
View Answer
Using the data that follows and assuming cost of goods sold is $273,700, prepare the cost of goods...... a... income statement (periodic inventory system). Include the amount of purchases for the month of October. Freight-in ................. $13,800 Merchandise inventory, Sept. 30, 2014 .........
View Answer
The following amounts appeared on Davison Company\'s adjusted trial balance as of October 31, 2014,...... a... sold, and gross profit, as well as the components and amounts of selling expenses and general and administrative expenses.2. Present a condensed single-step income statement that lists...
View Answer
Levesque Company makes and sells lawn mowers for which it currently makes the engines. It has an...... a... zero. Required a. Determine the maximum price per unit that Levesque would be willing to pay for the engines. b. Would the price computed in Requirement a change if production increased to...
View Answer
On January 1, 2011, Quick Stop, a convenience store, purchased a new soft-drink cooler. Quick Stop paid $25,780 cash for the cooler. Quick Stop also paid $1,090 to have the cooler shipped to its location. After the new cooler arrived, Quick Stop paid $1,810 to have the old cooler dismantled and...
View Answer
Transcribed Image Text
1 Boltzmann's Epitaph, an idea to die for!?! 2 At the beginning of the 20th century, Ludwig Boltzmann was one of the young physicists championing the particle view of matter. 3 Strange as it may seem now, the view was far from universal at that time, indeed it was not the favored theory of matter. The heavyweights of the time, 4 like Ernst Mach and others were strongly opposed to the idea and presented a strong resistance to the ideas at scientific conferences. 5 One unfortunate result of this was Ludwig Boltzmann's suicide at one such conference when he was still in his twenties. 6 His statistical formula for entropy is engraved on his headstone in memmory of his achievement and, perhaps, in mourning of 7 what might have been accomplished had he continued his work. 8 9 For a total of N particles, there are N! ways of arranging them: N choices for the first • (N-1) for the second .1 for the last 10 Without presenting a formal derivation, Boltzmann's formula for entropy is 11 S= klnw W = number of arrangements of the energy with = N! / [N1! N2! N3!.] W is called the partition function. If the N objects are placed in distinct groups, then each of these groups will have a number of arrangements calculated the same way. N1 objects in the first group can be arranged N1! Ways. These rearrangements do not affect the distribution of objects among the groups, so we divide the total N! arrangements by each of the Ni! Factors to get the number of arrangements with the same distribution. That is the Win Boltzmann's equation. 12 13 Basically, it says that the arrangement with the greatest entropy is the one which is most probable. 14 Recall that the change in entropy for an isolated system is always greater than zero. 15 So, isolated systems tend toward the most probable distribution of energy. 16 17 One application of this is for molecules with discrete energy states as required by quantum mechanics. 18 The fraction of molecules or population in each energy state can be determined using Boltzmann'sentropy. 19 20 Start with N molecules at temperature T and in some energy state En E_therm =1.5 NKT k= R/N_A 21 E_tot = N(1.5kT+En) 22 23 Via collisions and so on, the energy will not remain distributed this way. 24 25 We will suppose that the processes which redistribute the energy happen with no change in total energy 26 This is just saying that there is no energy input or output from the collection of molecules, 27 so that it is an isolated system. 28 29 So, picture an isolated collection of N molecules at temperature T and in the energy state En. No energy is exchanged with the surroundings. 30 [Q1] As some of them get bumped up into other energy states Ei, what happens to the thermal energy of the molecule? 31 We will use the thermodynamic definition of entropy: AS = dQ/T for reversible dQ (as it is here). We will count any change in thermal energy as heat. When a molecule changes energy state from En to Ei, the energy tied up in that form changes by Ei-En. Keeping in mind the statement on line 32, show that the heat associated with the transition is given by Q= -AE. 32 33 34 [Q2] 35 36 Using that result, show how the following relations come from Boltzmann's entropy equation (the first relation): 37 S= k In(W) e'S/k = W S=Q/T e^-AE/kt = W This exponential is the ratio of populations for two energy levels AE apart when at thermal equilibrium. 38 Now suppose you have 7 particles but only 11 units of energy. Find all possible distributions ( and the one with the highest value of W and therefore the maximum entropy). You may not need all the rows provided. Exercise: 7 particles =N 11 energy =E N! = 5040 EN 1 2 3 4 E n[(N_i)] W In(W) 7 3 4 11 144 35 3.555348 3.044522 4.65396 7 2 11 240 21 7 4 11 48 105 5040 8.525161 5040 8.525161 5040 8.525161 5040 8.525161 1 5040 8.525161 1 5040 8.525161 1 5040 8.525161 1 5040 8.525161 1 5040 8.525161 1 5040 8.525161 1 5040 8.525161 1 5040 8.525161 5040 8.525161 Q3: How does your most probable result compare to the exponential Boltzmann distribution? For a severely energy limited case, such as 7 particles and 9 energy units, the populations are limited to only the lower levels.
