A tank contains $50$ kg of a liquid at $25$ deg C$.$ At t $=0,$ valves are opened such that the same liquid at $80$ deg C flows in at $10$ kg$/$min through one pipe and it also flows in $(5$ kg$/$min$)$ at $50$ deg C in another pipe. A liquid stream $(15$ kg$/$min$)$ exits the bottom of the tank at temperature T$.$ The tank is very well mixed $($but with negligible shaft work$),$ very well insulated, and its contents always have a uniform temperature. a$.$ What is the temperature of the effluent liquid stream after these flows have been running for $5$ min? b$.$ How long does it take for the effluent stream to get

within $1$ deg C of its steady state temperature? $($ANS: $60$ deg C$,12\mathrm{.}7$ min$)$