P340 Lecture 3(Second Law)

THE FUNDAMENTAL POSTULATE (OF THERMAL PHYSICS)

• Any isolated system in thermodynamic equilibrium is equally likely to be in any one of its available microstates

THE SECOND LAW OF THERMODYNAMICS• Any isolated thermodynamic system will, with overwhelming

probability, evolve into the macrostate of largest multiplicity (consistent with the constraints imposed on the system) and subsequently will remain in that state.

P340 Lecture 3“Probability and Statistics”

• Bernoulli Trials• REPEATED, IDENTICAL, INDEPENDENT, RANDOM

trials for which there are two outcomes (“success” prob.=p; “failure” prob=q) – EXAMPLES: Coin tosses, queuing problems, radioactive

decay, scattering experiments, 1-D random walk,…

• A question of fundamental importance in these problems is: Suppose I have N such trials, what is the probability that I have “n” successes? The answer is:

P(n) = N!/[n!(N-n)!] pn(1-p)N-n

We will spend a bit of time looking at this distribution.

Meaning of , m s(Gaussian distributions)

http://en.wikipedia.org/wiki/Normal_distribution

Other Probability distributions(Poisson distributions)

http://en.wikipedia.org/wiki/Poisson_distribution

P(n)=ln e-l

= (m l mean)=s l1/2 (st. dev.)

This is very important in counting expts.

P340 Lecture 3(Second Law)

•We all know that if we see a movie in which a bunch of spilled water and broken glass on a floor spontaneously coalesce to form a glass half-filled with water that subsequently jumps up onto a nearby table, it is because the film is being run backwards. Is there a law of physics that provides this assurance because it is violated by the event as described, and if so, what is that law?

• Conservation of energy (1st law of TD): 2 responses• Newton’s second law: 2 responses • Second Law: 18 responses.

• It is NOT that energy conservation would be violated, the internal energy of the floor is far greater than that needed to lift the glass up onto the desk, but such internal energy cannot easily be converted into mechanical energy (indeed, one version of the second law simply states that it is impossible to build a machine whose sole function is to extract heat from a hot object and use that energy to perform work (such a device is called a “perpetual motion machine of the second kind”)).

Thermal interactions

I II

Consider two systems that are isolated from the universe, and each other, but then we allow them to exchange heat (i.e. energy exchange with no work done by either one on the other). What does the 2nd law tell us about this situation, and how might we analyse the relevant physics quantitatively?

Wall with a thermal conductivity that is changed from zero to non-zero

Thermal barrier

Thermal interactions

I II

Consider two systems that are isolated from the universe, and each other, but then we allow them to exchange heat (i.e. energy exchange with no work done by either one on the other). What does the 2nd law tell us about this situation, and how might we analyse the relevant physics quantitatively?

Wall with a thermal conductivity that is changed from zero to non-zero

Thermal barrier

The system evolves to the macrostate (i.e. division of energy between the two systems, since that is all we are allowing to change) of maximum multiplicity and stays there. (dW/dEI)V,E,VI= 0; what is the condition on the invidual subsystems that assures this mathematical result?