How Quantum Mechanics Changes Temperature

As the definition of particle and wave and position, so quantum mechanics warps the meaning of temperature, so that it is not a single well defined property, but has a meaning that depends on context. Indeed it is possible to have a range of temperatures inside a single space.
The most useful description of temperature is in terms of the random motion of particles in a space. The faster the random motion of particles, the higher the temperature, given by the equation  
\[\frac{1}{2}m \var\lt v^2 \gt } = \frac{3}{2} kT\]
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The temperature of the surface of the Sun is about 6000 Degrees Kelvin. The surface of the Sun is a plasma, and photons are repeatedly absorbed and emitted by electrons in atoms - photons and matter are in thermal equilibrium, both at the temperature of the surface of the Sun. When radiation from the Sun reached the Earth, it is still at this temperature, and when it passes through the Earth's atmosphere, the temperature is maintained. The Earth's atmosphere though is at a temperature of between 200 - 300 Degrees Kelvin, so light and matter have different temperatures inside the same space. This phenomena is possible because interaction of radiation and matter is limited, and is possible wherever interaction is limited

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