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## Main Question or Discussion Point

I must be missing some point with regards to the canonical Distribution. Let us imagine I have a closed (to energy and matter) box full of ideal gas at temperature T. The total energy in the box equals hence

E=3N2kT

, where N is the number of molecules, k Boltzmann's connstant.

Next, I allow the box to Exchange energy with a heat bath at, say, the same temperature T. Now the probability of having an energy E in the box follows Boltzmann's distributon, ∼exp−E/kT .

But if the energy in the gas contained in the box varies, also ist tempetrature will! The latter though should not, as coupling to the bath should yield isothermal conditions.

How can the energy vary if the temperature is constant??

What am I missing here?

Thanks

E=3N2kT

, where N is the number of molecules, k Boltzmann's connstant.

Next, I allow the box to Exchange energy with a heat bath at, say, the same temperature T. Now the probability of having an energy E in the box follows Boltzmann's distributon, ∼exp−E/kT .

But if the energy in the gas contained in the box varies, also ist tempetrature will! The latter though should not, as coupling to the bath should yield isothermal conditions.

How can the energy vary if the temperature is constant??

What am I missing here?

Thanks