Aquantum system has three states, with energies 0, 1.6 × 10-21, and 1.6 × 10-21, in joules. it is coupled to an environment with temperature 250 k. 1) what is the average internal energy?

To develop the problem it is necessary to apply two concepts, the first is related to the calculation of average data and the second is the Boltzmann distribution.

Boltzmann distribution is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. It is given by

Where,

energy of that state

k = Boltzmann's constant

T = Temperature

With our values we have that

T= 250K

To make the calculations easier we can assume that the temperature and Boltzmann constant can be summarized as

Therefore the average energy would be,

Replacing with our values we have

Therefore the average internal energy is

b.

explanation: