$(1)$ Consider the schematic for the cross section of the coat of a cow $($longhorn$).$ The internal temperatur of the animal is constant at $37$ degrees C$.$ Assume no heat is generated within the fat, skin and hair. Neglect radiation. $($a$)$ Calculate the temperature of the top surface of the skin $($hair$/$skin interface$).($b$)$ Calculate the temperature of the top surface of the skin if the longhorn is completely shaved as a prank. $($c$)$ Estimate how deep the skin$/$fat will freeze in part b$)$