A system has triply degenerate ground state with energy E0 and very large number of spaced states if T→ 0. Then partition function is _____(answer should be an integer)Correct answer is '3'. Can you explain this answer?

Question

A system has triply degenerate ground state with energy E0 and very large number of spaced states if T&rarr; 0. Then partition function is _____(answer should be an integer)Correct answer is '3'. Can you explain this answer?

Answer

If the system has a triply degenerate ground state with energy E0 and a very large number of spaced states, it means that there are three distinct states at the lowest energy level. This can occur, for example, if the system has three different possible orientations or configurations that all have the same energy.

Now, let's consider the temperature T. If T is very low compared to the energy spacing between the ground state and the excited states, then the system will predominantly occupy the ground state. This is because at low temperatures, the probability of occupying higher energy states is exponentially suppressed according to the Boltzmann distribution.

However, if the temperature is higher and comparable to the energy spacing between the ground state and the excited states, then the system will start to populate the excited states as well. The probability of occupying higher energy states increases with temperature, and eventually, at very high temperatures, the system will have a roughly equal probability of being in any of the available states.

In summary, at very low temperatures, the system will mainly occupy the triply degenerate ground state with energy E0. As the temperature increases, the system will start to populate the excited states as well, and at very high temperatures, all the available states will have roughly equal probabilities of being occupied.

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