### Re: Is there such thing as absolute heat?

Date: Mon Apr 13 14:16:50 1998
Posted By: Ronald Fisch, Physics, Washington University
Area of science: Physics
ID: 886548375.Ph
Message:
```
The equation
KE = m v^2 / 2
for the kinetic energy of the electron is only a good approximation
when v/c is small (where c is the speed of light).  The exact equation,
which comes from the Special Theory of Relativity and has been carefully
checked by many experiments, is
KE = m c^2 ( 1/sqrt(1 - (v/c)^2) - 1) .
Examining this equation, we see that the KE can become arbitrarily large,
even though v/c is always less than 1.

Actually, when you add energy to the electrons in an atom they become
unbound, and they escape.  When the electrons are bound very close to the
nucleus of the atom and moving very fast, their total energy is very small,
because the attractive (and therefore negative) potential energy between
the electron and the nucleus overwhelms the kinetic energy.  The thing
which prevents the electrons from falling downhill into the nucleus is
Heisenberg's Quantum Uncertainty Principle.

So you can see that the speed of light does not limit the energy of the
electrons.

```

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