An extreme thermos bottle might use silica aerogel as an insulator. Figure P14.70 demons...

An extreme thermos bottle might use silica aerogel as an insulator. Figure P14.70 demonstrates the insulating properties of the aerogel compound. Aerogel can protect human skin from a blowtorch at nearly point-blank range, made possible by its very low thermal conductivity (only 0.003 W/(m · K)) and a melting point of 1200°C. Let’s see if we can improve on the thermos bottle used by the author in Example 14.11, where we found that it took 1.2 h for his coffee to cool from 65°C to 55°C. (a) If the thermos bottle is a cylinder having an inner diameter of 7.0 cm, inner length of 12 cm, and wall thickness of 1.2 cm, what is the thermal conductance of the thermos material in the example? (b) If we replace the material with aerogel, how long will it take the coffee to cool the same amount? Assume the aerogel is coated with a thin protective layer of negligible thickness.