Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Question
Chapter 9, Problem 72E
To determine
The expression for average energy.
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P2D.8 Use the fact that (∂U/∂V)T = a/Vm2for a van der Waals gas (Topic 1C)to show that μCp,m ≈ (2a/RT) − b by using the definition of μ and appropriaterelations between partial derivatives. Hint: Use the approximation pVm ≈ RTwhen it is justifiable to do so.
In the canonical ensemble, we control the variables T, p, and N, and the fundamental function is the Gibbs free energy (G). But if we control T, p, and μ, then we will have a different fundamental function, Z (This is the case for cells that often regulate their temperature, pressure, and chemical potentials to maintain equilibrium). Which of the below options should the Z function equal?
H - TS - μN
H + TS + μN
H + TS - μN
G + μN
F - pV - μN
-H + TS + μN
It turns out van der Waals was very careful when “designing” the van der Waals equation: P = [RT / (Vm−b)] − (a / V^2m). If you’re not sure, let’s see why he divided the "a" term by V^2m and not Vm. Specifically, can you calculate the residual volume of an alternative equation of state: P = [RT / (Vm − b)] − (a / Vm) and show that the residual volume is -∞ L/mol
Chapter 9 Solutions
Modern Physics
Ch. 9 - Prob. 1CQCh. 9 - What information would you need in order to...Ch. 9 - Given an arbitrary thermodynamic system, which is...Ch. 9 - Prob. 4CQCh. 9 - Prob. 5CQCh. 9 - Prob. 6CQCh. 9 - Prob. 7CQCh. 9 - Prob. 8CQCh. 9 - By considering its constituents, determine the...Ch. 9 - Prob. 10CQ
Ch. 9 - Prob. 11CQCh. 9 - Prob. 12CQCh. 9 - Prob. 13CQCh. 9 - Prob. 14CQCh. 9 - Prob. 15CQCh. 9 - Prob. 16CQCh. 9 - Prob. 17CQCh. 9 - Prob. 18CQCh. 9 - Prob. 19ECh. 9 - Prob. 20ECh. 9 - Consider a room divided by imaginary lines into...Ch. 9 - Prob. 22ECh. 9 - The entropy of an ideal monatomic gas is...Ch. 9 - The diagram shows two systems that may exchange...Ch. 9 - A “cold” object, T1=300K , is briefly put in...Ch. 9 - Prob. 26ECh. 9 - Prob. 27ECh. 9 - Prob. 28ECh. 9 - Prob. 29ECh. 9 - Obtain equation (915) from (914). Make use of the...Ch. 9 - Show that equation (916) follows from (915) and...Ch. 9 - Using the relationship between temperature and M...Ch. 9 - Prob. 33ECh. 9 - Prob. 34ECh. 9 - Consider a simple thermodynamic system in which...Ch. 9 - Prob. 36ECh. 9 - Prob. 37ECh. 9 - Prob. 38ECh. 9 - Prob. 39ECh. 9 - Prob. 40ECh. 9 - Prob. 41ECh. 9 - Prob. 42ECh. 9 - Prob. 43ECh. 9 - Prob. 44ECh. 9 - Prob. 45ECh. 9 - For a room 3.0 m tall, by roughly what percent...Ch. 9 - Prob. 47ECh. 9 - A particle subject to a planet’s gravitational...Ch. 9 - Prob. 49ECh. 9 - You have six shelves, one above the other and all...Ch. 9 - Prob. 51ECh. 9 - Prob. 52ECh. 9 - Prob. 53ECh. 9 - Prob. 54ECh. 9 - Prob. 55ECh. 9 - Prob. 56ECh. 9 - Prob. 57ECh. 9 - Prob. 58ECh. 9 - Prob. 59ECh. 9 - Prob. 60ECh. 9 - Prob. 61ECh. 9 - Prob. 62ECh. 9 - Prob. 63ECh. 9 - Determine the density of states D(E) for a 2D...Ch. 9 - Prob. 65ECh. 9 - Prob. 66ECh. 9 - Prob. 67ECh. 9 - Prob. 68ECh. 9 - This problem investigates what fraction of the...Ch. 9 - Prob. 70ECh. 9 - Prob. 71ECh. 9 - Prob. 72ECh. 9 - Prob. 73ECh. 9 - Prob. 74ECh. 9 - Prob. 75ECh. 9 - Prob. 76ECh. 9 - Prob. 77ECh. 9 - Prob. 78ECh. 9 - Prob. 79ECh. 9 - Prob. 80ECh. 9 - Prob. 81ECh. 9 - The Debye temperature of copper is 345 K. (a)...Ch. 9 - Prob. 83ECh. 9 - In Exercise 35, a simple twostate system is...Ch. 9 - Prob. 86ECh. 9 - Prob. 87CECh. 9 - Prob. 89CECh. 9 - Prob. 90CE
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