Why can β not be linearly proportional to T, that is β = c o n s t a n t × T

Question

Why can   β not be linearly proportional to T, that is   β  =  c  o  n  s  t  a  n  t  ×  T

salumeqi · Accepted Answer

Because by convention, we want to write   β as the coefficient in front of energy E in the exponent   exp  ⁡  (  −  β  E  ). Exponents have to be dimensionless so   β has to have units of inverse energy. That&#039;s why it has to be objects such as   β  =  1      /    k  T because   k  T has units of energy. The latter statement holds because the energy per degree of freedom increases with the temperature. At the end, that&#039;s the fundamental answer to your question. The exponential is   exp  ⁡  (  −  E      /    k  T  ) because   E  ∼  k  T and &quot;hot&quot; means &quot;highly energetic&quot;. It&#039;s linked to the fact that the temperature has an absolute lower bound, the absolute zero, much like energy is bounded from below.

Why can β not be linearly proportional to T, that is β=constant×T?

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