a$)$ You are a trainee process engineer at a newly established distillery and have been asked to fabricate a pipe carrying hot vapors from the rectifying column to the condenser. The objective is to have the outer surface of the pipe at a maximum steady state temperature of $30C.$ Determine the inside temperature of the pipe $(T_1)$ as well as its thickness $L.$ Comment on the values

$[15$ Marks$]$