lecture24 - Lecture 24 Introduction to Statistical...

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Lecture 24 Introduction to Statistical Mechanics Statistical Mechanics handles very large systems of particles, for example the air in a room (of order 1 mole or 10 23 particles). As you’ll see such large systems are handled very diFerently than a single particle or a system of a few particles. If N is very large, tracking the position and velocity of every particle at every instant in time becomes very cumbersome and impractical. In many cases, we don’t even care where every little microscopic atom is at every instant in time. We care more about the macroscopic properties of the system, such as pressure, temperature, volume, and the number of particles in the system. Therfore, systems of many particles are treated in a fundamentally diFerent way from the systems we’ve discussed in the course so far. These systems are treated statistically ; in other words we describe them by their average properties. 1 “State” of a System ±or a system of 1 particle, we need 6 parameters to de²ne the “state” of the particle ( x, y, z, v x , v y , v z ). These six parameters give us the current location of the particle and enough information to predict it’s location at a later time. If we know the forces acting on a particle, we can specify it’s state for all future times. If we have a system of 2 particles, we need 12 parameters to describe the system. ±or N particles, we need 6N parameters If N is very large (like 10 23 particles in a solid or in this room), it’s completely impractical to track the location and velocity of every particle. Even with modern computers, we can’t do it. So, we instead describe a system with a large number of particles statistically. This way we don’t have to track the location of every particle at every instant. In this case, we don’t need to specify all 6N positions and velocities of every individual atom. Rather, we can describe the system by a few “macroscopic quantities” such as N, V, P, T. ±or the rest of the term, we’ll discuss this kind of system which is treated in a funda- mentally diFerent way from the systems we’ve discussed so far in this course. 2 Thermal Equilibrium You all have experience that energy ³ows from hot to cold. If you grab a glass full of hot tea, it burns your hand. That is the ³ow of thermal energy from the hot glass to your cold(er) hand. The thermal energy transfer between two systems depends on the temperature diFerence between them. This ³ow of energy due to temperature diFerence is called “heat” and given the symbol Q . Δ T 19
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As heat (thermal energy) fows From one system to another, the temperature oF each will change. There will be a fow oF energy between them until they are at the same temperature (called “thermal equilibrium). (DEMO) Why is this?
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This note was uploaded on 05/01/2008 for the course PHYS 13 taught by Professor Millan during the Spring '08 term at Dartmouth.

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lecture24 - Lecture 24 Introduction to Statistical...

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