A solid cube of mass m at a temperature $θ_0$ is heated at a constant rate. It becomes liquid at temperature $θ_1$ and vapour at temperature $θ_2$ . Let $s_1$ and $s_2$ be specific heats in its solid and liquid states respectively. If $L_f$ and $L_v$ are latent heats of fusion and vaporisation respectively, then the minimum heat energy supplied to the cube until it vaporises is
