4.) the complete equation for thermal conduction, allowing for time variations in temperature and internal heat sources is p coat/dt = k 22t/oz2 + a where k is the thermal conductivity, cp is the heat capacity, p is the density, and a is the heat production per unit volume. assuming that a is independent of time, the temperature gradient is purely vertical, and that the heat flow has reached a steady state condition (at/dt = 0),show that the temperature-depth distribution or geotherm will be given by the equation t(z) = az? + b + c where b and care constants. show and explain all intermediate steps in your derivation. how can the constants b and c be determined from temperature and heat flow measurements at the surface? given vlues of heat flow q, thermal conductivity k, and temperature to at the surface, give expressions for a, b, and c in terms of k, q, and to.