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Re: [Phys-L] heat content

The thermal energy appears on the left side of your equation 1. In the end, it appears that we agree. Calling energy in ocean water thermal energy to contrast it with the kinetic energy of the motion of macroscopic globs of water is exactly what I had in mind. I don't think it is an abomination to call that energy thermal energy either.

Push down on the piston on top of a metal cylinder of air at room temperature in a room surrounded by air at room temperature. Hold it down for a while and then bring the piston back up to its original position. Monitor the force on the piston as a function of position the whole time. Compare the work done on the gas during compression with the work done by the gas during expansion. One finds the latter to be smaller. Somebody explains that in doing work on the system, the person doing the work increased the thermal energy of the air in the cylinder. This increase in thermal energy was accompanied by an increase in the temperature of the air inside the cylinder. Some of the thermal energy flowed out of the air into the walls of the cylinder, and if one waited long enough, from the cylinder into the surroundings. I don't think it is an abomination to use the expression "thermal energy" in this manner.

Two carts are moving on one and the same straight horizontal frictionless track in one and the same direction. The trailing cart has a wad of clay on its front end and is moving faster than the leading cart. The trailing cart bumps into the lead cart and the two move off as one. Let the system be the two carts--including the wad of clay as part of the trailing cart. I don't think it is an abomination to say that some of the mechanical energy of the system prior to the collision is converted into thermal energy.

Someone tells me hold out my hand. I do. They put a potato at room temperature in my hand. They take it out of my hand and tell me the next few times this potato makes contact with my hand, it is going to have more energy. They say, "Close your eyes and see if you can tell me what kind." "Nonsense," I reply, "There is only one kind of energy." "Just try it," they respond. On one occasion, the person simply throws the potato at my hand. On another occasion he warms the potato in an oven and places it gently in my hand. My first point here is that, while I understand that in a broad general sense, there is only one kind of energy, I can tell the difference in how that energy manifests itself. As regards the terminology, I don't think it is an abomination to say that in the first case the potato had more motion-of-the-center-of-mass kinetic energy and in the other case the potato had more thermal energy.

Now suppose that unbeknownst to me, all along, a region of the potato had been hollowed out and in the hollow was a spring and a stick. When the person first put the potato in my hand the spring was unstretched. The third time after that that the person causes the potato to contact my hand, it is at room temperature and the ends of the spring have been attached to the ends of the stick such that the spring is stretched. The person puts the potato in my hand. I say, as far as I can tell the energy of the potato is the same as it was when I first held it in my hand. The person tells me to open my eyes and opens up the potato and shows me the spring. In this case, the person has increased the internal energy of the system without increasing the thermal energy. While I think that the expression "thermal energy" used as something that a system has, is a lot closer to being synonymous with "internal energy" energy than it is to an integral of TdS, there are times when I think saying "thermal energy" more clearly conveys what one means.



-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of John Denker
Sent: Monday, February 10, 2014 5:56 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] heat content

On 02/10/2014 03:18 PM, Jeffrey Schnick wrote:
I don't think you have to restrict the work term to zero to talk about
increasing the thermal energy.

I disagree. This is not a matter of opinion; The math backs up what I'm
saying. See below.

In terms of your example of the
baby bottle, with some water in it, standing at rest on a table, if
you tilt the nipple over by pushing the tip of it to one side without
changing the orientation of the rigid part of the baby bottle you
increase the elastic energy of the system,

That's not a P dV term within the usual meaning. Please let's keep things
connected to

dE = - P dV + T dS [1]