Does specific heat change with volume?
No, the specific heat capacity is a constant which is characteristic of a material, not of the amount of material.
The units of specific heat capacity, Joules per gram per degree, allow us to see how come a larger amount of substance will experience a smaller increase in temperature for the same amount of heat energy put into the substance.
We use the equation Q = m c delta-T
where Q = the heat energy, in Joules
m = the mass of the material being heated or cooled, in g
c = the specific heat capacity, in J/g/^oC
delta-T = change in temperature, in ^oC