Is Mass Dependent on Temperature According to Mass-Energy Equivalence?

[DrStupid]

The individual particles have different "gammas". I already pointed out this mistake.

The particles have different gammas because they have different velocities. I do not see the problem.

 

[PAllen]

$$m_{0i}=m_p+\gamma_{ei}(v_e) m_e-u_i$$ (for ONE atom)

From the above, it DOES NOT follow that, for a system of atoms:

$$M=\Sigma{\gamma'_i m_i}-U$$

I think part of this is simply definition of U, independent of any pairwise model, such that it can even apply to non-linear interactions. You have a system of particles 'at infinity'. As they come together and bind, radiation is released. The mass of the system is reduced by the radiation released/c^2 (else conservation violated). We call this released energy = mass deficit * c^2 = binding energy = U by convention. U is generically a function of the system as a whole, with a maximum value defining the ground state of the system.