$2\mathrm{.}2$ Using the example given in Problem $2\mathrm{.}1,$ calculate the temperatures of the two exposed surfaces $($the 'hot' and 'cold' sides of the barrier$).$ Check the Biot number to demonstrate that this is an example of a 'thermally thin' material. What would the surface temperatures be if the barrier was $50$ mm thick? Calculate the Biot number for this situation. What are your conclusions?