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Basically the word Temperature (in Kelvin) of the body is the average Kinetic Energy of molecules in a body.

Zero Kelvin is understandable that all molecules kinetic energy is Zero

But what is Negative Kelvin, means negative kinetic energy ? How can a body will have negative energy ?

PRANEEL
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2 Answers2

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Zero Kelvin is understandable that all molecules kinetic energy is Zero

But what is Negative Kelvin, means negative kinetic energy ? How can a body will have negative energy ?

As explained on this Wikipedia page, (formally) negative temperatures can result for systems with bounded phase space.

What this means is that the entropy decreases when the energy increases.

This is probably easiest to understand for the finite discrete system of $N$ non-interacting two-level atoms (having level energy $\pm \epsilon$) discussed on the Wikipedia page.

The temperature can be calculated exactly as: $$ \frac{1}{T} = \frac{1}{2}\ln\left(\frac{N+1-E}{N+1+E}\right)\;, $$ where, for simplicity, I set $k=\epsilon=1$, so the value of $E$ ranges from $-N$ to $N$. The temperature is zero when $E=0$ and the temperature is negative when $E$ is positive.

You can start to understand this, for example, by considering the highest energy state. Just like the lowest energy state, the highest energy state is perfectly ordered, having all atoms in the upper state. Thus, just like the lowest energy state, the highest energy state also has zero entropy. Thus, as we approached the highest energy state from below the entropy must have been decreasing.

In this bounded system the entropy is actually largest when $E=0$, therefore the entropy decreases when either $E$ increases away from zero (negative temperature) or when $E$ decreases away from zero (positive temperature).

hft
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Temperature is not the same thing as kinetic energy. Temperature is, by definition, the reciprocal of the derivative of the entropy of the system with respect to energy. In some cases the only energy is kintic and then your assumption is true. However , whenever the entropy decreases as energy increases, the system has a negative temperature. The standard example is a system of spins in an external magnetic field. When the temperature is infnite the orientation of the spins is random. If you add energy to the system the numbers of states available decreases and the entropy decreases and the temperature becomes negative. Thius a negative temperature is in some sense one that is hotter than infinite rather than cooler tha zero. This sounds crazy, but it makes sense because the the definition involves a reciprocal.

mike stone
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