A sugar cube (left(L_{o}=1 mathrm{~cm} ight)) is dissolving in a cup of tea. The mass transfer coefficient,

A sugar cube \(\left(L_{o}=1 \mathrm{~cm}\right)\) is dissolving in a cup of tea. The mass transfer coefficient, \(k_{c}\), to the tea is \(5.0 \times 10^{-5} \mathrm{~m} / \mathrm{s}\). You may assume lumped capacitance is valid. The molecular weight of sugar is 342.3 and its density is \(1580.6 \mathrm{~kg} / \mathrm{m}^{3}\). The concentration of sugar in the tea, \(c_{\infty}\) is effectively zero. How long will it take the cube to dissolve away?