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PHYS 213 Midterm Exam HKN Review Session
Steven Kolaczkowski Alex Littlefield
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First Law of Life Check your units
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First Law of Thermodynamics
Check Your Units dπ=ππ+π π ππ =dQβPππ If volume is constant: dπ=ππ
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Entropy, Temperature, and the Second Law of Thermodynamics
CHECK YOUR UNITS πβ‘ π π΅ lnβ‘(Ξ©) where Ξ© is the number of microstates Ξ© π‘ππ‘ππ = Ξ© 1 β Ξ© 2 β΄ π π‘ππ‘ππ = π 1 + π 2 ππ= 1 π ππ+ π π ππβ π π ππ For an Isolated system Ξπβ₯0 or Ξ π ππππ£πππ π β₯0 If Ξπ=0 the process is reversible Temperature: 1 π β‘ ππ ππ π,π
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Equilibrium and Counting Microstates
We will observe the macrostate with the most microstates (maximum entropy) A microstate is an observable state Distinguishable: Ξ©= π π Indistinguishable: Ξ©= π π π! π π‘ππ‘ππ is maximized when T is constant across system (thermal equilibrium)
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Heat Capacity and Latent Heat
Heat capacity: the amount of energy required to raise the temperature of a material by 1K πΆ π = ππ ππ = π½ πΎ π π£ πππ = 1 π dπ dπ = π½ πππβπΎ π π£ πππ π = 1 π ππ ππ = π½ ππβπΎ πΆ π£,π‘ππ‘ = πΆ π£,1 + πΆ π£,2 ππ= πΆ π£ βdπ=π π π£ πππ π βππ = π½ Latent Heat: The amount of energy needed to transition between states of matter T does not change during a phase change! πΏ π = Ξ π π ππππβππππ’ππ π π ππππ = π½ ππ πΏ π£ = Ξ π ππππ’ππβπππ π ππππ’ππ = π½ ππ
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Ideal Gases and Equipartition
CHECK YOUR UNITS Equipartition: The idea that thermal energy on average is distributed equally among all quadratic modes of motion <πΎ>= π π΅ π 2 for each quadratic degree of freedom Monoatomic Gases: Diatomic Gases: Solids: 6 Mass doesnβt matter for calculating energy, but it does for finding average velocity Ideal Gas Law: Assuming that particles will not collide or interact with each other, only with the walls of the container, and are volumeless Works best with low densities and high temperatures (a few, fast moving particles) ππ= 2 3 π<πΎ > π‘ππππ =πππ=ππ
π
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Solids, More Heat Capacities, and Internal Energy
CHECK YOUR UNITS π=π<K> Ideal Solids π π‘ππ‘ππ =π < 1 2 π π£ 2 > π‘ππππ +< 1 2 π π 2 > =2π<πΎ > π‘ππππ =3π π π΅ π We will assume that ideal solids are incompressible ππ=ππ and π πππ = 1 π ππ ππ =3 N A k B
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Boltzmann Distributions and Quantum Oscillators
βThe best thing in the worldβ-V, 2018/4/7 For a Quantum Oscillator, energy is discretized by π=hf and π π =ππ= π π΅ π=qhf Total number of states given N oscillators and q energy quanta Ξ© π,π = πβ1+π ! π! πβ1 ! π=π ln Ξ© Ξπ(πβπ+1)=π ln π+π π+1 βπ π π π = dπ dπ β ππ πβπ Probability of State having energy πΈ π : π πΈ π = π β πΈ π π π΅ π π Partition function: π= Ξ£ πππ π π‘ππ‘ππ π β πΈ π π π΅ π REMEMBER TO TAKE INTO ACCOUNT DEGENERACY!!! βActually the Partition function is my favorite thing in the worldβ-V, 10 mins later R S
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More 213 Stuff Atmospheres: Ξπ=ππβ therefore π β π 0 = π β ππβ π π΅ π and <β> = π π΅ π ππ βYou get this from the Boltzmann distribution, the best thing in the worldβ-V, 30mins later
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Exam Advice When doing problems, PLEASE PLEASE PLEASE CHECK YOUR UNITS!!! You will be shocked how many questions you can solve just matching units and having an idea of what they are asking for Know when and how to use your equation sheet Donβt panic, just keep on moving Make sure you are in the right mindset going into the exam Spend your time showing what you know DONβT CHEAT
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Spring 2015
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Spring 2018
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Spring 2015
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Spring 2018
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Spring 2015
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Fall 2014
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Spring 2018
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Fall 2014
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Fall 2014
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