Specific Heat of Solids|What is Specific Heat of Solids ?|Definition

Einstein (1907) first applied Planck’s Quantum hypothesis to resolve the discrepancies of the classical theory of specific heat of solids. According to classical Dulong-Petit’s law the gram-molecular specific heat of all solids are the same value that is 6 calorie per degree centigrade per mole at above room temperature. Classical theory assumes that each atom behaves as a three-dimensional oscillator vibrating about their mean position of rest. Corresponding to each cartesian component of vibration there are two degrees of freedom, translational and rotational. Again according to the theorem of equipartition of energy, the mean kinetic energy associated with each degree of freedom is $\displaystyle \frac{1}{2} kT$

where K is the Boltzmann constant and T is the Absolute Temperature. Hence the energy associated with each component is $\displaystyle \frac{1}{2} kT+\frac{1}{2} kT=kT$

. So the mean energy associated with the above oscillator is,

$\displaystyle \left \langle \epsilon \right \rangle=3kT$

Total energy per gram-mole of the solid is,

$\displaystyle E=N\left \langle \epsilon \right \rangle=3NkT=3RT$

where N is the Avogadro number and $\displaystyle R=Nk$

, the universal gas constant the specific heat of the solid is, therefore,

$\displaystyle c_{v}=\frac{dE}{dT}=3R\sim 6\ cal/^{0}C/mole$

This is Dulong-petit’s law of specific heat of solid which hold good at Higher temperature only. Experiment on Ag,Ge and Si shows that $\displaystyle c_{v}$

decreases with the decrease of temperature and tends to zero. The discrepancy was resolved by Einstein and then Debye by using the quantum theory proposed by Max Planck.

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