Conceptual
Describe what a two-state paramagnet is and why it is covered in this chapter.
A two-state paramagnet is a material where its particles tend to align parallel to any externally applied magnetic field. We used it as a physical example of a two state system that we could calculate micro/macro states and multiplicities from.
(We will be seeing more of paramagnets)
Calculate the number of possible 5-card poker hands, dealt from a deck of 52 cards. (The order of cards doesn't matter). A royal flush consists of the five highest-ranking cards (A, K, Q, J, 10) of any one of the four suits. What is the probability of being dealt a royal flush?
Total multiplicity = 2.6e6
Multiplicity of getting royal flush = 4
Probability = 1.54e-6
Describe the second law of thermodynamics in words not using multiplicity, entropy, or disorder.
The number of possible arrangements particles can have in a system will always tend towards the maximum
What is the multiplicity of an Einstein solid with N = 3, q = 6? Describe what this means
28
There are 28 different ways that 6 units of energy can be split between 3 oscillators
Physically, what are the microstates of an Einstein solid?
Each possible way the energy can be arranged between the oscillators.
Problem 2.8
(a) 21
(b)6.89e10
(c)0.0145%
(d)12.4%
(e) If all the energy started in 1 solid or the other, it would irreversibly move towards the energy being shared between them
What are the macrostates of an ideal gas?
The total energy, volume, and particles in a system.
Problem 2.29
Most likely (qA = 60): 264.4
Least likely (qA = 0): 187.5
Long time scales (all accessible): 267.0
Describe why burning gasoline would increase the total entropy of the universe and be considered an irreversible process?
When you burn gasoline, not only do you convert a smaller number of relatively large hydrocarbon molecules into a larger number of relatively small exhaust gas mole- cules, but you also release a great deal of thermal energy (converted from chemical energy) into the environment. This energy can arrange itself in many ways among the surrounding atoms, so the entropy of the environment increases a great deal as this thermal energy spreads farther and farther.
Problem 2.39
S = 573 J/K
4.5x as indistinguishable helium atoms