A hot-air balloon achieves its buoyant life by heating the air inside the balloon, which makes it less dense than the air outside. Suppose the volume of a balloon is 1800m3 and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required life. Assume that the outside air temperature is 0oC and that air is an ideal gas under these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind).