Definition -
Specific heat of solids is the measure of the number of degrees of freedom .
The specific heat of a substance is defined as the heat energy absorbed by one unit mass of the substance to raise its temperature by one degree .
While measuring the specific heat either volume or pressure is kept constant . But in case of solids , we usually speak of the specific heat at constant volume and is given as -
Cv =( ∂Q/ ∂T)v = (∂E+P ∂V)/dT =( ∂E/ ∂T)v
The electronic contribution to specific heat is very small at room temperature and hence we speak of only the specific heat by lattice only
Partial derivative is taken since E may be the function of other quantities , subscript v shows that volume is kept constant .
Whenever energy is added to a solid , the increase in its energy occurs in two ways , firstly the energy is used to vibrate the lattice very vigorously and secondly the free electrons in the metals and semiconductors may be excited to higher energy levels . Therefore ,
C(solid )= C(lattice) + C (electronic )The electronic contribution to specific heat is very small at room temperature and hence we speak of only the specific heat by lattice only
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