Today I was studying a bit of thermodynamics and I came up with a doubt . Let us assume an adiabatic container with an adiabatic wall separating the container into two equal parts . First part contains a monoatomic gas at a fixed temperature and the other part contains a diatomic gas at a temperature lower than the first one. When the wall is removed suddenly then in my book it is written that the mixture will atain a particular fixed temperature . But I think that when the wall will be removed then the molecules having different kinetic energies collide with each other and exchange energies among themselves and a particular temperature will be reached when the velocities of the two different gaseous molecules will become equal. But why will that temperature will remain fixed , i mean why not will the temperature changes further? As even if both the gases have same temperature they have different internal energies . I think they should go on exchanging energies
Actually you are right when you say that the two system will go on exchanging energies. Different degrees of freedom usually equilibrate over different times. However, after waiting some time, the system will get a new thermodynamic equilibrium where averages will stay constant again. And will remain constant both, the kinetic energy per particle of the two components, which must also be equal, since they represent the temperature of the two subsystems. But also the two potential energy, as well as the inter-species internal energy, must remain constant, although for the potential energy there is no reason to be the same for each component.
Of course, one has to remember that thermodynamic equilibrium means that average values are constant but accompanied by continuous fluctuations whose relative size goes to zero by increasing the size of the system. Thus, thermal equilibrium means that the average kinetic energy is fixed, but individual velocities of the particles do have a statistical distribution (for classical systems the famous Maxwell-Boltzmann velocity distribution).