(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The diagram below shows a one-dimensional row of 5 microscopic objects each of mass 410-26 kg, connected by forces that can be modeled by springs of stiffness 26 N/m (so each object can be modeled as if it were connected to a single spring of effective stiffness 4ks = 104 N/m -- neglect any possible differences for objects near the ends). These 5 objects can move only along the x axis.

Use these precise values for the constants:

hbar = 1.054610-34 J ยท s (Planck's constant divided by 2)

k = 1.380710-23 J/K (the Boltzmann constant)

What is one quantum of energy for one of these objects?

Delta E = 5.37743e-21 correct check mark J

Using the Einstein model, calculate the entropy of this system for total energy of 0, 1, 2, 3, 4, and 5 quanta.

q = 0: S = 0 correct check mark J/K

q = 1: S = 2.22215e-23 correct check mark J/K

q = 2: S = 3.73900e-23 correct check mark J/K

q = 3: S = 4.90887e-23 correct check mark J/K

q = 4: S = 5.86590e-23 correct check mark J/K

q = 5: S = 6.67745e-23 correct check mark J/K

Calculate to the nearest degree the average absolute temperature of the system when the total energy is in the range from 3 to 4 quanta. (You can think of this as the temperature when there would be 3.5 quanta of energy in the system, if that were possible.)

T3 to 4 = 561.88730 correct check mark K

Calculate to the nearest degree the average absolute temperature of the system when the total energy is in the range from 4 to 5 quanta. (You can think of this as the temperature when there would be 4.5 quanta of energy in the system, if that were possible.)

T4 to 5 = 662.61229 correct check mark K

Calculate the heat capacity per object when the total energy is 4 quanta. (Think of this in terms of increasing from 3.5 quanta of energy in the system to 4.5 quanta of energy in the system, if that were possible.)

C4 = 1.067745e-23 correct check mark J/K/object

If the temperature were raised very high, classically what would we expect the heat capacity per object to be for this one-dimensional system? Give a numerical value.

Chigh T = ??? wrong check mark J/K/object

(One reason for the discrepancy is that the high-temperature limit assumes that the number of oscillators is large (N >> 1), which is not the case in this tiny system.)

2. Relevant equations

C= deltaE/deltaT

classical limit of 3k = 4.210-23 J/K/atom

3. The attempt at a solution

I got all the questions except the last one which I've already tried searching for clues in the internet.

I tried 3kN= 3*1.380710e23*5 but got it wrong.

I thought it was just supposed to be 3k like in the relevant equation but that's wrong maybe because N=5??

I also thought that 3 in the 3k equation has something to do with 3 springs, so I tried 2*k instead of 3*k but got it wrong too.

Please help.

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# Homework Help: Physics: Specific heat capacity of a solid

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