In 1906, in what is arguably the first paper in theoretical condensed matter physics [3], Albert Einstein postulated that…

In 1906, in what is arguably the first paper in theoretical condensed matter physics [3], Albert Einstein postulated that…

Question:

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In 1906, in what is arguably the first paper in theoretical condensed matter
physics [3], Albert Einstein postulated that vibrational excitations of a solid are
quantized with energy ho, just like photons in the vacuum. Repeat his calculation
for diamond: calculate the energy E(T) of one mole of simple harmonic oscillators
with characteristic frequency w at temperature T and show that the specific heat
capacity is
where
dE
Cy(T) = = RF
dT
F(x):
ha
KBT
(2) ²
x/2
(sinh(x/2).
and R = NAVKB, the product of Avagadro’s number NAV and Boltzmann’s constant
kB. Plot C(T) and show that it deviates from Dulong and Petit’s law, Cy = (R/2) per
quadratic degree of freedom, at temperatures T << hw/kB. Expert Answer: Answer rating: 100% (QA) To calculate the energy E T of one mole of simple harmonic oscillators with characteristic frequency at temperature T we can use the formula E T N Avo View the full answer