Introduction

In a black body cavity at temperature T, there are multiple oscillators with different energy levels. The energy levels of these oscillators are given by E = nhv, where n represents the energy level and v represents the frequency of the oscillator. The total number of oscillators and the average energy of the oscillators can be calculated using these energy levels.

Calculation of Total Number of Oscillators

To calculate the total number of oscillators, we need to sum up the number of oscillators at each energy level. Let's assume the total number of oscillators in the cavity is N.

At energy level 0 (n=0), there is only one oscillator denoted by N0. At energy level 1 (n=1), there are N1 oscillators. Similarly, at energy level 2 (n=2), there are N2 oscillators.

Therefore, the total number of oscillators N can be calculated as the sum of the number of oscillators at each energy level:

N = N0 + N1 + N2 + ...

Calculation of Average Energy of Oscillators

The average energy of the oscillators can be calculated by summing up the product of the energy level and the number of oscillators at that energy level, and then dividing by the total number of oscillators.

Let's denote the average energy of the oscillators as E_avg.

E_avg = (0*N0 + 1*N1 + 2*N2 + ...)/N

Effect of Planck's Constant on Average Energy

As Planck's constant (h) tends to 0, the average energy of the oscillators would also tend to 0. This is because Planck's constant is directly proportional to the energy of the oscillator.

When Planck's constant is very small, the energy levels of the oscillators become very small as well. As a result, the average energy, which is the sum of the product of energy levels and the number of oscillators at each level, would also become very small.

In the limit as Planck's constant tends to 0, the energy levels of the oscillators would approach 0, resulting in an average energy of 0. This means that the oscillators would have negligible energy and would not contribute significantly to the overall energy of the system.

Conclusion

In a black body cavity at temperature T, the total number of oscillators can be calculated by summing up the number of oscillators at each energy level. The average energy of the oscillators can be calculated by summing up the product of the energy level and the number of oscillators at that level, and then dividing by the total number of oscillators. As Planck's constant tends to 0, the average energy of the oscillators also tends to 0, indicating negligible energy contribution from the oscillators.