banner with logos

graph described below

Temperature Entropy Graph

This figure is a graph of entropy vs. temperature for Ferric Ammonium Alum (FAA). The horizontal axis is temperature in degrees Kelvin, from 0 to 3. The vertical axis is Entropy, in a unitless form created by dividing the specific entropy by the gas constant R. This dimensionless entropy runs from 0 to 2.

The graph shows:

Entropy at Low Magnetic Field

When the temperature is zero, the entropy of the FAA is zero. (Any perfect crystal at absolute zero has zero entropy.) Entropy rises quickly with temperature. By about 0.5 Kelvin, the entropy has leveled off at the natural log of 6 (about 1.8), which value it keeps to the top of the graph.

Entropy at High Magnetic Field

At zero Kelvin, entropy in high magnetic field is also zero. As the temperature rises, the high field entropy rises more slowly than the low field entropy. (The applied magnetic field imposes order on the molecular magnetic moments and thus limits their entropy.) By 3 Kelvin, the high field entropy has climbed to about 1.1, or about two thirds of the low field entropy at that temperature.

Ideal ADR Cycle

The changes in temperature and entropy that the salt pill undergoes during the cycle can be plotted as a path on the temperature-entropy graph. The cycle has 4 sections:

Non-Ideal Cycle

The non-ideal cycle is the same as the ideal cycle except in part 4 and the end of part 3, when it is dumping the heat to the heat sink. The non-ideal cycle is not shown by vertical line, that is, the process does not happen at constant temperature. At the end of segment 3, the warm up, the non-ideal path goes to a higher temperature. By raising the salt pill temperature to a higher temperature than the heat sink, the operators can dump the heat more quickly (though the process is not quite as efficient.) They turn on the heat switch before the salt pill reaches its highest temperature, though, and heat starts flowing into heat sink before they stop ramping the temperature up. Because the heat starts flowing before the salt pill finishes warming, the non-ideal path curves from segment 3 to segment 4. In the ideal cycle, there is no curve, only a sharp corner, since the ideal heat switch can turn on instantaneously when the ideal salt pill reaches the temperature of the heat sink.

The non-ideal cycle also differs from the ideal at the end of the heat dumping part of the cycle. The non-ideal cycle intersects the high magnetic field entropy curve, and follows it down in entropy and temperature to the point where it intersects line segment 1. This represents the fact that the non-ideal cycle continues to dump heat into the heat sink as the magnetic field begins to ramp down.

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