The specific heat capacity of a metal at low temperature \((T)\) is given as \(C_p(\mathrm{kJK^{- 1}kg^{- 1}}) = 32\left(\frac{T}{400}\right)^3\) . A \(100\mathrm{g}\) vessel of this metal is to be cooled from \(20\mathrm{K}\) to \(4\mathrm{K}\) by a special refrigerator operating at room temperature \((27^{\circ}\mathrm{C})\) . The amount of work required to cool the vessel is