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therm1 - Physics 53 Thermal Physics 1 Statistics are like a...

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Physics 53 Thermal Physics 1 Statistics are like a bikini. What they reveal is suggestive; what they conceal is vital. — Arthur Koestler Overview In the following sections we will treat macroscopic systems that are in thermal equilibrium . Most of our discussion will center on the behavior of gases. We will use appropriate macroscopic variables, some of which are already familiar, such as density, volume and pressure. We will usually assume the CM of the system is at rest, and that molecular velocities are randomly distributed as to direction, so there is no bulk flow or velocity field to consider. There may be energy (kinetic or potential or both) internal to the molecules themselves, if they are not monatomic. The total kinetic energy of the random molecular motion, plus any energy the molecules may have internal to themselves, constitutes the internal energy of the system. This is one of the new macroscopic variables we will use in our description. Thermal equilibrium, temperature and the Zeroth Law Macroscopic variables used to describe the state of a system in thermal equilibrium are called state variables . Density, volume and pressure are state variables, as is internal energy. We will introduce two more as we go along: temperature and entropy. What is meant by thermal equilibrium is this: If the system is in thermal equilibrium, state variables all have definite values. Since the state variables all represent averages of some kind, what it means to have a “definite value” is that the fluctuations which might make the average uncertain are small enough to be ignored. In a statistical situation, such fluctuations are generally inversely proportional to the number of particles. In systems of macroscopic size that number (roughly Avogadro’s number) is extremely large, so the fluctuations are tiny. Most of the possible situations a system may be in are not states of thermal equilibrium. Nevertheless, it is an experimental fact that a system left to itself evolves toward thermal equilibrium . (How that happens is still not fully understood in detail.) The PHY 53 1 Thermal Physics 1
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time it takes for a non-equilibrium state to evolve to equilibrium is called the “relaxation time”. It varies from case to case, but is often quite short by human standards. Two macroscopic systems can exchange energy with each other. This exchange can be accomplished by collisions among particles at a common interface, or by other methods such as emission and absorption of electromagnetic radiation. If energy exchanges can take place, we say the systems are in thermal contact . Such exchanges generally disrupt, at least temporarily, the states of equilibrium of the two systems. It may happen, however, that two systems brought into thermal contact undergo no disruption of equilibrium in either system. Then we say the systems are in equilibrium with each other .
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