For bacteriological testing of water supplies and in medical clinics, samples must routinely be incubated for 24 h at 37C. A standard constant temperature bath with electric heating and thermostatic control is not suitable in developing nations without continuously operating electric power lines. Peace Corps volunteer and MIT engineer Amy Smith invented a low-cost, low-maintenance incubator to fill the need. The device consists of a foam-insulated box containing several packets of a waxy material that melts at 37C, interspersed among tubes, dishes, or bottles containing the test samples and growth medium (food for bacteria). Outside the box, the waxy material is first melted by a stove or solar energy collector. Then it is put into the box to keep the test samples warm as it solidifies. The heat of fusion of the phase-change material is 205 kJ/kg. Model the insulation as a panel with surface area 0.475 m, thickness 9.85 cm, and conductivity 0.0120 W/m . C. Assume the exterior temperature is 24.0C for 12.0 h and 18.0C for 12.0 h. (a) What mass of the waxy material is required to conduct the bacteriological test? kg (b) Explain why your calculation can be done without knowing the mass of the test samples or of the insulation.