This question involves the process of firewalking in which a firewalker walks across a bed of hot coals and claims there are no burns to his feet. $($Disclaimer: Don't try this yourself!$).$

$($a$)$ Calculate the heat transferred by conduction into the sole of one foot of a firewalker given that the bottom of the foot is a $3\mathrm{.}00-$mm$-$thick callus with a conductivity at the low end of the range for wood and a skin density of $300$kg$/$m$3.$ The area of contact is $25\mathrm{.}0$cm$2,$the temperature of the coals is $700$Cand the time in contact is $1\mathrm{.}00$ s$.$

$($b$)$ What temperature increase is produced in the $25\mathrm{.}0$cm$3$of tissue affected?

$($c$)$ What effect do you think this will have on the tissue, keeping in mind that a callus is made of dead cells?