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Re: [Phys-l] PV question

On 24 Jan 2010, John Mallinckrodt wrote:

Bernard Cleyet wrote:

A PID controller with a heater or cooler of a single reservoir won't do?

John Mallinckrodt wrote:

(e.g., an isobaric or isochoric process), you will need a large number (technically, an infinite number) of reservoirs at different temperatures.

That could work to perform a reasonable approximation of a quasi-static process on the gas, but it wouldn't constitute even an attempt to perform a reversible process because heaters and coolers generate entropy by design.

John Mallinckrodt
Cal Poly Pomona

It is conceivable that an ideal controllable heat sink/source (reservoir) could be placed in thermal contact with the system executing a desired quasistatic process. I'll conceive one to demonstrate the truth of this statement.

Consider a large quantity (relative to the system being programmed) of a chemically pure gas confined to a cylinder fitted with a piston. The closed end wall of the cylinder should be thermally conducting, but the other walls and the piston are thermally insulating and of negligible heat capacity. (The latter condition is not strictly necessary, but it will simplify discussion.) The piston is fitted with a variable force transducer capable of moving the piston.

The conducting end wall of this device can now be placed in thermal contact with the system under consideration. The desired process may now be executed by controlling the positions of the system piston and the reservoir piston independently. So long as these operations are performed quasistatically the process will be reversible. Note that a phase change in the reservoir (i.e. condensation of the gas) will affect the temperature range over which it can operate, but aside from practical considerations this system + reservoir has two degrees of freedom that can be used to execute any process on a system that has an equation of state f(P,V,T) = 0, and do so reversibly.