In 1906, in what is arguably the first paper in theoretical condensed matter physics [3], Albert...

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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. 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.

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To calculate the energy ET of one mole of simple harmonic oscillators with characteristic frequency at temperature T we can use the formula ET NAvogad... View the full answer