Dear Colleagues, I am trying to "design" the simplest sort of phenomenon that demands the concept of entropy. My first description left many ambiguities which I have attempted to correct in this revision. Unfortunately, the revision has gotten horribly long. Still, I am hoping that at least a few of you -- as you love me -- will respond. Here is the prompt.
Our goal is to juxtapose two bodies of air, of equal temperature and volume but different histories to see which can exert the most pressure. Thus we hope to separate the effects of temperature, per se, from the effects of how that temperature was arrived at. We start with a single cylinder of air at one bar (roughly sea-level pressure) and 50 degrees C, which contains three slidable/peggable dividers. One is installed at the exact middle of the cylinder, the other two at opposite ends. All motions of the sliders will be quasi- static (infinitely) slow). The cylinders and the sliders are designed to be adiabatic—no heat or mass can pass through them—except in the following two respects. Just to the right of the central slider are installed two ports, one through which air may be admitted or released and a second through which heat may enter or depart through conduction. These ports will always be assumed to be adiabatically sealed unless explicitly described otherwise. Finally, on either side of the central slider is installed a temperature sensor so that we may know the temperature within the two chambers. With this equipment in hand, we begin the preparation of the two juxtaposed chambers. On the left, we push in the slider until the left chamber reaches a temperature of 20 degrees C. and we peg it there. We measure the distance from the left slider to the central slider . Now, we open the heat and air ports on the right side of the central slider and we push in the right slider until it is the same distance from the central slider as the left slider is on the other side. (Thus we have guaranteed that the volume of the two adjacent chambers is the same) Now we close the air port. Through the still open heat port we admit just enough heat to bring the temperature up to 20 degrees C. and then we seal it. So now we have, as planned, two adjacent chambers, of equal temperature and volume. Now we unpeg the central divider. Which way, if any, does it move and why? -- nick
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