PS1 - Chemistry 135: Problem Set #1 Due Tuesday September...

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Unformatted text preview: Chemistry 135: Problem Set #1 Due Tuesday September 28, 2010 Please show all the work and reasoning that is relevant. How you got your answer is often more important at than the answer itself. Also, I suggest you don’t “overthink” the problems. They are not meant to be complex, but just a simple (often “back of the envelope”) calculations relevant to work, energy, etc. Suggested reading: Chang, Chapter 1 and 3; Smith, Chapter 1; Levine Chapter 1 and 2.1 1. The library’s potential energy and power In the library, there are lots of books. For each book, someone has done work against gravity to put the book on a bookshelf. If a book falls off the shelf, this potential energy is turned into kinetic energy. (a) When a book hits the ground, what happens to the kinetic energy? (Hint: we know that energy is conserved, so it must go somewhere . . . ) (b) If a book weighs 1kg and there are 50 books on a shelf and 20 shelves in the library, how much potential energy is there in the library (in terms of books on shelves)? Assume that the acceleration due to gravity is 10 m/s2 and that the shelves are all 1 m high. 1 Joule = 1 kg × 1 m/s2 × 1 m. (c) If we had a team of really quick librarians who could re-shelve the books in a minute and then we continuously dropped all the books once a minute, how much power (energy/time) could we generate? (1 Watt = 1 J/s). 2. Math review Here are two problems to remind you about the differences between complete and partial derivatives. This will be an important set of concepts for understanding what’s to come in the rest of the course. Consider the volume of a prolate elipsoid (football shape) as a function of its length ￿ and radius r: 4 V (￿, r) = π￿r2 3 Here, we will analyze how the volume V changes as we change the radius r in two ways. (a) Calculate dV /dr (i.e. the total derivative of V with respect to r). Hint: You cannot assume that d￿/dr is zero. (b) Calculate the partial derivative ∂ V /∂ r. If you’re not familiar with partial derivatives, Wikipedia has a nice brief summary of them ( and in particular how they differ from complete derivatives. 1 3. “Quickies” (a) Niagara Falls and the first law of thermodynamics Joule suggested that the water at the bottom of the Niagara Falls, which are 50m high, should be warmer than that at the top. Estimate the rise in temperature. The heat capacity of 1 mol water (which weighs 0.018 kg) is 80 J K−1 . The acceleration due to gravity is 9.8 m s−2 . (b) The power of chocolate How high can a person (assume a weight of 70kg) climb on one ounce of chocolate, if the heat of combustion (628kJ) can be converted completely into work of vertical displacement? (c) Our friend the mole When I was a student, I always wondered why “23” in 6.02 × 1023 . It always seemed like a really big number and was never really justified. Well, here you get to work out an explanation. If I tell you that: • a mole of water weighs 18g • the density of water is 1g/cm3 ˚ • a single water molecule has a volume of about 1 A3 How many molecules are there in a mole. Work the problem based upon the numbers given here; these numbers are approximate, so you won’t get exactly the number you’re likely famliar with)? 2 ...
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This note was uploaded on 10/17/2010 for the course CHEM 135 taught by Professor Pande during the Spring '10 term at Stanford.

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