Entropy of a quantum sized material

AI Thread Summary
The discussion focuses on calculating the entropy of a quantum-sized material with specific energy levels and total energy. The user is confused about determining the value of "N" in the multiplicity equation, initially assuming it to be 18 based on the total energy and energy level spacing. Despite this assumption, their calculations did not yield the correct entropy value. The user seeks clarification on whether their approach is valid and if the multiplicity equation is necessary for solving the problem. The thread highlights the challenges in applying statistical mechanics concepts to quantum systems.
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Homework Statement


A small material has quantum oscillator energy levels 2E-23 J apart. Suppose the material has a total energy of 34E-23 J and contains 5 atoms. Find the entropy of the material.


Homework Equations


Entropy = (Boltzmann's constant)*ln(multiplicity)

Multiplicity = (q + N - 1)!/[q!(N-1)!]


The Attempt at a Solution


I'm having trouble grasping the question. The 5 atoms are understood, but I'm having trouble finding the "N" for the multiplicity equation.

So, I came up with N = 18, because the total energy is 34E-23 J and the energy levels are 2E-23 J apart, and q = 5.

Then applying the multiplicity equation and plugging it to entropy, I didn't get the correct answer.

Am I on the correct path to find N, or do I even need the multiplicity equation?
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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