An ice cube of mass 0.1 kg at $0^0\mathrm{C} \mathrm{is} \mathrm{placed} \mathrm{in} \mathrm{an} \mathrm{isolated} \mathrm{container} \mathrm{which} \mathrm{is} \mathrm{at} {227}^0\mathrm{C}. \mathrm{The} \mathrm{specific} \mathrm{heat} \mathrm{S}$of the container varies with temperature T according to the empirical relation S = A+BT, where A = 100 cal/kg-K and B = $2\times {10}^{-2}\mathrm{cal}/\mathrm{kg}-{\mathrm{K}}^2.$ If the final temperature of the container is ${27}^0\mathrm{C},$ find the mass of the container.

(Latent heat of fusion for water = $8\times {10}^4 \mathrm{cal}/\mathrm{kg}, \mathrm{specific} \mathrm{heat} \mathrm{of} \mathrm{water} = {10}^3 \mathrm{cal}/\mathrm{kg}-\mathrm{K})$