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Unformatted text preview: Answers to Physics 176 One-Minute Questionnaires Lecture date: January 20, 2011 What is the difference between “properties of a macroscopic sys- tem do not depend on history” versus “properties have to be in- dependent of time”? I gave an example of this in class: a block of wood is an example of a macro- scopic system that can be time independent but its properties are dependent on its history, e.g., how it was produced by the tree. Any macroscopic solid that has some persistent non-uniform structure would be similar to wood in this regard; the rigidity of a solid prevents the atoms from mixing over human time scales so the history is frozen in. The way to create a history-independent equilibrium solid would be to start with a liquid phase (if a liquid phase exists, this would not be the case for wood) and very slowly cool the liquid until it crystallizes into a solid. The slow cooling allows atoms to move around and eliminates the frozen structure. What are some objects that would seem to be not in equilibrium that actually are (if any)? Not sure how to answer this question since it depends on what you mean by “seems to be”. A quick answer is that truly equilibrium systems are almost never found on Earth on a day-to-day basis, one has to work really hard in a lab to arrange for objects to be in equilibrium. What are more examples that don’t reach equilibrium in the same way the sandpile is not in equilibrium? Are there other way equi- librium is not reached? There are many ways that a system can be out of equilibrium beyond not having a constant temperature, not having a constant pressure, etc. For example, the speeds of molecules in an equilibrium gas have to obey a uni- versal distribution called the Maxwell speed distribution (see Section 6.4 on page 242 of Schroeder). It is possible to temporarily change the speed distribution of a gas to be inconsistent with this distribution, e.g., shoot a monoenergetic beam of particles into the gas. The gas would then be out of equilibrium but in a way that is hard to detect. 1 Could you explain more about the condition for equilibrium that the pressure P has to be the same everywhere, except if there is an external field? What happens in an external field? One condition for a macroscopic system to be in thermodynamic equilibrium is that all macroscopic properties are time independent. This in turn implies that the net force on any macroscopic part of the system must be zero, else that part of the system will start to move. For a body in the absence of any external fields like a gravitational field, forces inside bodies arise from pressures being applied to virtual surfaces and so the requirement for mechanical equilibrium is that the pressure is the same everywhere inside the body. In the presence of an external field, the pressure has to balance the forces from the external field....
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