Consider a system consisting of a gas, it is put in a container which is permits transmission of all kinds of electromagnetic waves. If this system is isolated and put in a perfect vacuum, and left for sometime, will it achieve absolute zero? I think so because every particle above absolute zero will emit thermal radiation(energy) in the form of em waves, since our boundary permits em waves to travel through it ,our system is constantly loosing energy , so as per law of conservation of energy the kinetic energy must decrease and finally all particles must stop moving( characteristic of absolute zero).
So , am I correct? Correct me please if iam wrong!
Best Answer
You seem to make the implicit assumption that your vessel is placed in an environment that does not emit any thermal radiation, i.e. is already at 0 K temperature. The temperature of your container will asymptotically decrease to 0 K but will never actually reach it.
Assuming black-body radiation, fixed heat capacity $c$, and sufficient thermal conductivity, the temperature will decrease as $dT/dt = -A\sigma T^4/c$, with $\sigma=5.67\times10^{-8}~\mathrm{WK^{-4}m^{-2}}$ the Stefan-Boltzmann constant and $A$ the external area of the container. The temperature will decrease over time as $\propto t^{-1/3}$, which is rather slow.
Update If you want to do the calculation more precisely, you'd first have to put a prefactor for the emissivity of your gas, as a function of temperature. Typically, gases at reasonable densities in man-like volumes have an emissivity very close to zero. Moreover, at some point, the gas would condense on the walls of your container (I think around 20 K for hydrogen and 4 K for helium, and much higher than that for anything else), which would turn your "gas in a container" into a much more difficult "solid state on a container wall" problem.
Only once you've figured out all that, you can start to wonder about more fancy quantum mechanics such as the probability that the entire crystal lattice makes the transition from its first excited state to the global ground state via a radiative transition. I'd wager that it will take more than the age of the universe to get there.
Update 2 Let's see how long it will take to approach the ground state. Suppose that the container has a size $L=1$ m; the lowest-energy transition is the one for a phonon with a wavelength equal to $L$. If the speed of sound in the condensed material is v=1 km/s, then the relevant temperature for the last transition to the ground state is $T_1=hv/(Lk_B)$=50 nK. If the emissivity of the gas is $\epsilon$, the time to reach the final temperature from an initial temperature $T_0$ is $$ t = \frac{c}{3A\sigma\epsilon}\left(\frac{T_0}{T_1}\right)^3. $$ If I plug in some numbers, e.g. 1 kg of air (c=1 kJ/K), emissivity 1e-3 (wild guess), T1=50 nK, T0=300 K, A=1 m2, then I find t=1e+42 s, i.e., 1e+34 years. Yes, longer than the age of the universe before the quantum mechanics of the ground state start to play a role.