dW = Fds = pAds = pdV W = pdV

We defined heat capacity C and specific heat c (heat capacity per mass) as:
Q = C ΔT = c m ΔT
For water, c = 1cal/g o C = 1 Btu/lb o F = 4187 J/kg K
The molar specific heat is the heat capacity per mole.
However, the amount of heat needed to
raise the temperature of 1 mole by
1 kelvin depends on whether we
perform the operation at constant
pressure or at constant volume:
Q = n C P ΔT or Q = n C V ΔT
In both cases, Q= ΔE int +W:
ΔE int is the same, but W is not!
Consider a process at constant volume, raising the
temperature by ΔT . Q = n C V ΔT
Q= ΔE int + W
W = 0 !
Q = ΔE int = (3/2) nR ΔT = n C V ΔT
→ C V = (3/2)R = 12.5 J/molK
→ E int = n C V T
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