A “miserly” system (with negative heat capacity) can be in thermal equilibrium w
ID: 2061123 • Letter: A
Question
A “miserly” system (with negative heat capacity) can be in thermal equilibrium with other systems, but this equilibrium is often unstable: small fluctuations in energy can cause a cascade effect. Consider a miserly system M which is in thermal equilibrium with another system B. Describe what happens when, due to fluctuations, a small amount of heat moves from M to B, in the following three cases:(I) System B is another miserly system
(II) System B is a normal system with a much larger (in magnitude) heat capacity than M (III) System B is a normal system with a much smaller (in magnitude) heat capacity than M No numbers necessary in this problem; just describe what happens.
Explanation / Answer
Most physical systems exhibit a positive heat capacity. However, even though it can seem paradoxical at first,there are some systems for which the heat capacity is negative. These include gravitating objects such as stars; and also sometimes some nano-scale clusters of a few tens of atoms, close to a phase transition. A negative heat capacity can result in a negative temperature.
According to the virial theorem, for a self-gravitating body like a star or an interstellar gas cloud, the average potential energy UPot and the average kinetic energy UKin are locked together in the relation
Upot= -2Ukin
The total energy U (= UPot + UKin) therefore obeys
U= -Ukin
If the system loses energy, for example by radiating energy away into space, the average kinetic energy and with it the average temperature actually increases. The system therefore can be said to have a negative heat capacity.
Describe what happens when, due to fluctuations, a small amount of heat moves from M to B, in the following three cases:
(I) System B is another miserly system
(The system will remain in equilibrium as in steady state both systems are getting heat and their kinetic energy is increasing but total energy is constant)
(II) System B is a normal system with a much larger (in magnitude) heat capacity than M
The euillibrium of the system will be mainatined as there is no change in the system B
(III) System B is a normal system with a much smaller (in magnitude) heat capacity than M No numbers necessary in this problem; just describe what happens.
The euillibrium will be disturbed as kinetic energy if both B & M will increase.
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