Foundations of Quantum Mechanics and Physical Chemistry
Prof. Sanctuary talks about Science
E-Books for post-secondary education
Ebooks have hit Kindles, ipods and other devices in many areas, including education. There are lots of programs out there for young children, but fewer for higher education. For example in teaching freshman chemistry at McGill, we are high tech. We have huge screens; power point slides; internet access (my son Skyped me once when I was teaching 600 students, much to their amusement); I can pull up Wikipedia, or any other programs, (I like the phet Physics simulations); we have clickers (so the students can vote on questions asked in class), and the whole kit and caboodle is recorded so the students do not even have to attend the lectures.
Yet they have to buy a text book which costs about US$175 (In Canada). In our two classes there are 1100 students. Multiply by the average of 5 courses students usually take and you can see that books are a major expense. And this is just one class. Do the math, and students shell out a lot.
Then there are the tons of trees that are sacrificed. Our text for freshman chemistry weighs 3 kg (6.6 lbs)! Money-conscious students usually sell their texts and the second hand market blossoms. After about three years, the book is down to $50 or so and the book companies start to lose their market. If it were a regular book, then when a print edition runs out more are printed if needed, but not in the text book market. Although new editions appear with claims of new improvements and corrections, the dominant reason for a new edition is to get the market back. If the book was selling like hot cakes, then new editions are rarely contemplated.
You cannot copy protect hard copy.
The text that the team teaching our course chose is General Chemistry by Petrucci et al and is in it 10th edition! The only changes I noted from the 9th were the addition of a few more problems. The general rule to justify a new edition is that it should have about 20% new content. This is rarely the case.
Companies desperate to hold onto their market share, inundate teachers with the plethora of “resources”, such as a web site (usually not good and not used much by students anyway); other multimedia; solution manuals; and study guides. These are considered a necessary burden by text book companies, but they jack up the price.
It should not be this way and today, with computer technology, the heavy environmentally unfriendly hard copy text books should be rejected by teachers in favour of ebooks, if available.
The developing world needs these books too, but cannot afford them, so they ignore copyrights and make them out of cheap paper and sell them for a few dollars.
I believe it is long overdue to do away with hard copy text books altogether, along with their high cost, and adopt ebooks.
Think of the advantages: no paper, nothing to ship, can be updated so users always have the latest edition, integrated into the internet, easy to copy protect, and can be sold for a fraction of the price of hard copy. No resale market.
Moreover the usual hard copy text contains way too much material for a two semester course–with about a thousand pages. Ebooks can readily be broken up into modules which are focused on the material needed for a course. As one of the authors of Physical Chemistry by Laidler Meiser and me, we got the copyright from Houghton Mifflin and have made it into a copy protected pdf with built in multimedia popups, and an extensive free solution manual on-line. Although the full ebook is available, there are six modules covering thermo, electrochem, kinetics, quantum, stat. mech., and solids and liquids. The starting price is only $14.99, (a 5 month license) a far cry from $150 plus. A semester course is usually four months, so a 5 month license fits the needs of many students.
Copy protection is essential and we have developed an MCHPDF viewer that takes any number of books in pdf format and secures them. That is the PDF viewer acts like a library of copy protected ebooks, with license expiry and updates built in. Give us your pdf ebook and we will give you royalties much greater than anything offered by a text book company.
However one of the most exciting aspects of ebooks is to reach the developing world. Many just cannot afford paper. Even if individuals cannot afford to buy their own copy, governments, organisations and universities can instead obtain a fixed number of licenses at a reasonable cost, making the ebooks available to millions of people.
Today it is natural for students to read and study from a computer. When I compare ebooks with hard copy, I can find nothing to favour the latter over the former. What’s your take on this?
Entropy (Part 6): Randomness and ensembles
After rolling 2, 3, 4, 10 and Avogadro’s dice, as seen in the entries below, it becomes clear that the most random states (most number of ways of rolling a number) always dominate while those with fewer arrangements occur less frequently:
1 Entropy: Randomness by rolling two dice
2 Entropy: Randomness by rolling three dice
3 Entropy: Randomness by rolling four dice
4 Entropy: Randomness by rolling ten dice
5 Entropy: Randomness by rolling Avogadro’s dice
In this final entry of randomness and entropy, the concept of an ensemble is discussed.
We are using a die to represent a particle that has six states that come up randomly. Hence we have treated systems with 2, 3, 4, 10 and Avogadro’s constant (let’s use 1023) of particles (dice) and have shown that as the number increases, the total number of accessible states, is given by 6n. Clearly the number of states in Avogadro’s case is 61023 : an enormous number!! If you start to roll this many dice, every roll gives an outcome in exactly the same way as for 2 or 3 dice: just add up all the rolls (it will take a bit of time!! but it is still a specific number). However when your roll, and if you could add them all up, the answer would be always very close to 3.5×1023 (see end). This is clearly because the total number of accessible states, W, can be replaced by the total number of random accessible states, Wrandom that all have outcomes clustered around 3.5×1023 .
Each time you roll that many dice, it is unlikely they will come up in any arrangement other than the ones that give the value of 3.5×1023 .
We call the collection of all those arrangements that give the most probable outcome an Ensemble. In French ensemble means a collection.
The ensemble concept is useful in statistical mechanics. So now let us think of a gas moving around in a container at 300 K. We could take repeated snap shots of the gas, and every time we would see the particles frozen in different position. We could also measure the speed of each particle (in principle). Each snap shot is like a roll of Avogadro’s dice. Below there are three of the many different arrangements and these will arise because each is consistent with a value of 300 K.
If the were not consistent with a temperature of 300 K such a state would be very improbable and can be neglected.
Consider he following is an ordered state:
This state is possible but it is not consistent with 300 K. In fact if the 5 balls are distinguishable, then there is only one way to arrange these. Since Boltzmann’s equation of the entropy is
S=klnWrandom
then since in that ordered state W = 1, then the entropy of that state is zero (ln(1)=0) which means perfect order.
In contrast, let us calculate the entropy of rolling 61023 dice (and treat them as particles). In this case the entropy is given by S = kln(61023) = 1.8xkx1023 . Let us use the value of Boltzmann’s constant, k=1.3806503×10-23 J K-1 which gives the entropy of S = 2.48 J K-1 . This is the value of the randomness of the gas.
Suppose we have a system of two bulbs joined together with a closed stop cock. On one side the gas has 1023 particles, each with 6 states giving 61023 accessible states. Let us suppose that the empty bulb is the same size and is under the same conditions, so when the stop cock is opened, the number of accessible state increases to 61023 x 61023 . For this larger system there are many, many more accessible states and the gas will move into the evacuated bulb and occupy those states randomly. The entropy must increase. I will not do that calculation, because we need to take into account that the particles are indistinguishable, but it was from these considerations that Boltzmann determined his equation (Probabilities multiply but the entropy adds, so the only function that has this property is the logarithm.)
When Boltzmann was explaining this, Poincaré pointed out that for a finite system (fixed number of dice) it will eventually return to its original state (Poincaré recurrence theorem or ergodic theory). Apparently to this, Boltzmann replied:
“You should live so long!”
Most probable roll:
- 2 dice: (12-2)/2+2=7
- 3 dice: (18-3)/2+3=10.5 or 10 and 11 because we deal with integers only
- 10 dice: (60-10)/2+10=35
- 1023 dice: (6×1023- 1023)/2+1023 = 3.5×1023
The interactive software used in this video is part of the General Chemistry Tutorial and General Physics Tutorial, from MCH Multimedia. These cover most of the topics found in AP (Advanced Programs in High School), and college level Chemistry and Physics courses.
Bryan Sanctuary, a Professor of Chemistry at McGill University (Montreal, Canada), is the primary author of this blog as well as president of MCH Multimedia. | www.mchmultimedia.com | and co- author of Physical Chemistry - Laidler, Meiser, Sanctuary
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