$14\mathrm{.}2-1.$ Temperature Response in Cooling a Wire. A small copper wire with a diameter of $0\mathrm{.}792$ mm and initially at $366\mathrm{.}5$ K is suddenly immersed in a liquid held constant at $311$ K$.$ The convection coefficient h $=85\mathrm{.}2$ W$/$m$2$ K$.$ The physical properties can be assumed constant and are k $=374$ W$/$m $$ K$,$ cp $=0\mathrm{.}389$ kJ$/$kg $$ K$,$ and $=8890$ kg$/$m$3.$

Determine the time in seconds for the average temperature of the wire to drop to $338\mathrm{.}8$ K $($one$-$half the initial temperature difference$).$

Do the same but for h $=11\mathrm{.}36$ W$/$m$2$ K$.$

For part $($b$),$ calculate the total amount of heat removed for a wire $1\mathrm{.}0$ m long.