You are in South Africa, and are employed by a mining company to mine gold in the famous deep vein systems of what was once Rhodesia (Cecil Rhodes got very very rich on this gold… yes, Rhodes of Rhodesia, and Rhodes of the Rhodes scholarships). The mine is 13,000 feet deep and you are working on this deepest level. The temperature gradient there is a typical 25°C/km, the rock is typical with a thermal diffusivity of 1 mm²/s, the mean annual temperature at the surface is 20°C, and the total annual temperature swing at the surface is 30°C. 

• What is the mean annual temperature at the level in the mine in which you are working? (please show a diagram of the problem as you are setting it up)