Given the graph below of the envelope that encloses all temperatures measured over the course of many days in the summer, using thermistors at many depths into a borehole in a rock surface,

(a) Estimate the length scale, z*, just by inspection of the graph. This length scale arises in setting the rate of decay of the amplitude of the temperature swings with depth. Show me this depth on the plot. Note: you can do this with no knowledge of the formula for z*.

(b) Also estimate the thermal diffusivity, k, of the rock: (and this time show me your formula!)

   

Transcribed Image Text:

0 Z*-20 Depth (cm) 40 60 80 100 120 140 -10 -5 0 5 T T₂ + e²¹T₁ 15 amp T+T S 10 Temperature (°C) amp 20 25 30