The heaters inside a winter cabin suddenly fail. Heat is lost to the outdoors the rate of 150 kJ/h, and the electric appliances inside generate 75 kJ/h of heat. The air is initially at 100 kPa and has temperature 30°C with a volume of 10 m3. How long will it take to reach an air temperature of 0°C? (cv = 0.717 kJ/kg-K for an ideal gas @ 300 K). Hint: In reality, the mass of air in the cabin will increase with time. As the air inside cools, it will contract and draw in air from the environment. For simplicity, assume the mass of air inside the cabin is constant, and equal to the mass initially inside.