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Shaun Harlow
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I am only aware that the formula has to do with entropy/thermodynamics. I could really use the help on how it applies in physics and what the formula is really about.
Shaun Harlow said:I am only aware that the formula has to do with entropy/thermodynamics. I could really use the help on how it applies in physics and what the formula is really about.
stevendaryl said:In that equation, [itex]S[/itex] is the entropy and [itex]E[/itex] is the energy. In thermodynamics, temperature can be defined as:
[itex]\frac{1}{T} = \frac{dS}{dE}[/itex]
So your inequality just says [itex]T \gg 0[/itex]. So the temperature is well above absolute zero.
Shaun Harlow said:So the inequality is saying that the temperature is above zero? If so, you talk of the "bizarre notion" of a negative absolute temperature that some people infer, but that is not possible correct?
stevendaryl said:That definition of temperature assumes that entropy increases with energy (so [itex]T[/itex] is always positive), which is true for classical thermodynamics, but for systems with a discrete number of states, it's possible for [itex]S[/itex] to decrease with [itex]E[/itex], which leads to the bizarre notion of a negative absolute temperature.
stevendaryl said:The symbol [itex]\gg[/itex] means "much greater than". So the temperature isn't just positive, it's pretty high.
Negative temperatures are not possible in classical thermodynamics, but there are quantum systems where a negative temperature is possible. A negative temperature means that the entropy goes down instead of up when the system gets more energy.
The formula 1/(dS/dE)>>0 represents the idea that a small change in energy (dE) will result in a large change in entropy (dS). In other words, the rate of change of entropy with respect to energy is very high, meaning that a small change in energy will have a significant impact on the overall system.
This formula is often used in the field of thermodynamics to understand how energy and entropy are related. It can also be applied to other areas of science, such as chemistry and biology, to analyze the relationship between energy and the disorder of a system.
One example of this formula in action is in the production of electricity. When coal is burned to generate electricity, there is a large increase in energy, but also a significant increase in entropy as the chemical bonds in the coal are broken down. This formula helps to quantify the relationship between the two changes.
This formula is applicable to any situation where there is a relationship between energy and entropy. However, it is most commonly used in situations where the change in energy is relatively small compared to the change in entropy. In these cases, the value of 1/(dS/dE) will be much greater than 0.
A large value for this formula indicates that a small change in energy can cause a dramatic change in entropy. This has important implications for understanding and predicting the behavior of systems, as even small changes in energy can have a significant impact on the overall state of the system.