A $0\mathrm{.}8$ mm diameter copper wire $)$ at an initial temperature of $150C$ is quenched in water at $35C,$ with heat transfer coefficient, $h=85\mathrm{.}5\frac{W}{m^2}.C.$ Show step by step calculations to determine the following;

a$.$ Characteristic length of the copper wire, $L_c$ in m $.$

b$.$ Biot number, Bi$.$

c$.$ Reciprocal of time constant, $b.$

d$.$ Time required $($in seconds$)$ by the wire to reach a temperature of $95C.$