solve problem (c)

= a) By considering the heat balance between time t and t+dt of a slab of unit area at depth z and thickness dz, show that its temperature changes at a rate given by: at OPT at Oz? b) Assume that the temperature at the soil-air interface varies with time as T(0,1)=To + asinwt and that heat flow in and out of the solid is only by conduction. Show that the temperature at depth z is: T(2,1)=T,+ a(z)sin or D where D=2(x/6) a(z)= a(0)exp(-2/D) (you can start by differentiating left hand side of T(z,t) equation with respect to t and the right hand side twice with respect to z) c) For a typical soil, K = 0.3 x 106ms. Over a period of one year, calculate D and hence find the peak-peak variation of temperature at depths of 1m, 3m, and 5m for the cases To=15C, a(0) = 20C. (=, +( D