Statistical Physics Problem 1a - MIT OCW

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In summary, the professor is suggesting that the student try solving the equations for t using the zeroth law of thermodynamics, which states that if two systems are in equilibrium, then their coordinates are the same. The student should then try to solve for P'' from the two equations.
  • #1
ehrenfest
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[SOLVED] statistical physisc

Homework Statement


http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/AC9B128C-9358-4177-BFE6-A142E0FD897B/0/ps4.pdf
I am working on Problem 1a. I am really confused about this question. Do I set the two equations equal to each other and solve for something? Do I just randomly write down 3 equations for t in terms of the respective variables of the 3 systems and then plug the given equations into to them to see if they are equal?

Homework Equations


The Attempt at a Solution

 
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  • #2
Try assuming the gases are ideal and use the correct equation of state. Did you read the lecture notes?
 
  • #3
Yes, I read the lecture notes. Speaking of that, go here http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/D4B27A47-C2E6-4D06-B646-177DC744CC2A/0/lec10.pdf
In the third slide, why is the predictor t = c_g PV/N and not t = c_g PV/NT ? It seems like they want the same constant whenever the system is in equilibrium, so doesn't that mean they want the same constant regardless of what T is at equilibrium.
In the current problem, they say the coordinates of the system are P and V, so I assume that means N is constant. So, can I define t = PV-nbP, t'' = P''V'' and then the first equation makes t = t'' at equilibrium, but I have no idea what to do about the second equation? Should I just guess and check or is there a systematic way to do this? Is there only one answer?
 
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  • #4
If temperature is the predictor of thermal equilibrium, then is it better to define the predictor to be t = c_g PV/N or t = c_g PV/NT for an ideal gas? It seems to me that the first one is a better match for the ideal gas law PV = nRT. The other way doesn't make much sense from a dimensional point of view.

But I see now that you don't need to assume ideal gases in problem 1a. Use the zeroth law: if A and C are at equilibrium and B and C are at equilibium, then A and B are at equilibium. Try calculating P'' from the first equation and from the second equation and setting the values equal to each other. Use your definitions t = PV-nbP and t'' = P''V'', and t' should emerge.
 

Related to Statistical Physics Problem 1a - MIT OCW

1. What is Statistical Physics?

Statistical Physics is a branch of physics that uses statistical methods and probability theory to study the behavior of large systems of particles. It aims to understand the macroscopic properties of a system by looking at the microscopic behavior of its individual components.

2. What is MIT OCW?

MIT OCW (OpenCourseWare) is a free and open online publication of course materials from the Massachusetts Institute of Technology. It provides access to lectures, problem sets, exams, and other resources from various courses offered at MIT.

3. What is the purpose of Statistical Physics Problem 1a on MIT OCW?

The purpose of Statistical Physics Problem 1a on MIT OCW is to introduce students to the basic concepts and techniques of statistical physics. It covers topics such as probability distributions, ensembles, and thermodynamic potentials, which are essential for understanding the behavior of physical systems at the macroscopic level.

4. Is prior knowledge of physics required for this problem set?

Yes, prior knowledge of physics is necessary for this problem set. It is recommended that students have a strong understanding of classical mechanics, thermodynamics, and basic calculus before attempting this problem set.

5. How can I use Statistical Physics Problem 1a on MIT OCW to improve my understanding of statistical physics?

To improve your understanding of statistical physics, you can use this problem set as a practice tool to apply the concepts and techniques learned in class. It is also helpful to review the solutions and explanations provided by the instructors to gain a deeper understanding of the material. Additionally, you can use online resources or consult with a tutor or professor for further clarification on any challenging concepts.

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