Show that specific heat of the solids is C=3R

 consider a block having N atoms which cant hav translatory nd rotatory motion . the atom vibrating along a line (X-axis) ll hav kinetic nad potential energy . thus , it has 2 degrees of freedom . bt since it can also vibrate along Y nd Z - axis . so it has 6 degrees of freedom ....

by law of equipartition of energy , energy of each atom = 6 * 1/2 kT = 3kT

thus , energy associated with N atoms = U = 3NkT

but , N*k = R .......... so U = 3RT 

differentiating wrt T

C_v = dU/ dT = 3R

i hope u got it ...