specific heat in solids and liquids I read a text which said:
specific heat of liquids and solids in constant pressure and constant volume does not differ a lot.
can some one explain it more?
 A: You may find a table of specific heats e.g. at

https://en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities

Look at the last column, for example. Almost all the specific heats are between $0.5 R$ and $4 R$, mostly around $2R$. This may be basically explained by each atom's or molecule's having something comparable to $2$-$3$ harmonic oscillators inside. Each of them contributes $R$ or so to the specific heat and the inner structure of the atom/molecule doesn't matter for the energetic considerations.
A: For an arbitrary material, $dU=C_vdT-PdV$.  If the material is incompressible, dV --> 0, so $C_v=\frac{dU}{dT}$.  We also know that $H=U+PV$ and $C_p=\left(\frac{\partial H}{\partial T}\right)_P$.  For an incompressible material, this gives $$C_p=\left(\frac{\partial H}{\partial T}\right)_P=\frac{dU}{dT}+P\frac{\partial V}{\partial T}=\frac{dU}{dT}=C_v$$
Since liquids and solids are nearly incompressible, this is why their heat capacities at constant volume and at constant temperature are nearly the same.
