(a) While shopping at a thrift store, you purchase a cheapwater-heater. The heater has a total surface area of 3 m3 which youdecide to insulate using a special kind of insulation material withconductivity of 0.08 W/m K. For normal operation, you want tomaintain the inside surface of the insulation at 75C while theoutside is at 20C. Additionally, you want to limit heat transferloss to 200 W. Given your requirements, how thick does theinsulation need to be?
(b) The heaters on a Space X spacecraft suddenly fail. Givenyour expertise insulating thrift store waterheaters, you are calledin to help. You discover that without the heaters, the spacecraftis losing heat via radiation at a rate of 100 kJ/h. The onboardsystems generate heat at 75 kJ/h. The air within the spacecraft isat a temperature of 25C and a pressure of 100 kPa, and occupies a10 m3 volume. Your job is to determine how long it will take beforethe air temperature within the spacecraft reaches - 20C.
