The specific heat at constant pressure, c p is defined as the partial derivative c p = ∂ ∂ T h | p . However, it is not independent of c v , they are related by the Mayer equation, c p − − c v = − − T ( ∂ ∂ T p ) 2 / ∂ ∂ v p = T v α α 2 / κ κ T . Then the two partials of the vdW equation can be used to express c p as c p ( v , T ) − − c v ( T ) = R 2 T v 3 R T v 3 − − 2 a ( v − − b ) 2 ≥ ≥ R Here in the limit v → → ∞ ∞ , c p − − c v = R , which is also the ideal gas result as expected; however the limit v → → b gives the same result, which does not agree with experiments on liquids.