1. To the Amazon (EPM = Evil Physics Monkey) With his limited resources the EPM decides that the best way to get to his chosen destination (the Amazon rain forest) is by hot air balloon. The monkey makes a giant balloon out of garbage bags, fills it with air, and seals it tight. He then makes a harness to hold a large Tupperware bin underneath and climbs inside with his new favorite device, a cordless, solar powered hair dryer. The giant balloon has a volume of 100 m3 The Evil Physics Monkey fills the balloon outside in the summer, where the temperature is 30 C.
a) How many moles of air are in the balloon? The combination of monkey, scimitar (don't leave home without it), "basket," harness, blow drier, munchies, and balloon have a mass of 100 kg. The balloon expands as the air inside it expands.
b) How hot does the air inside of the balloon have to be to rise off the ground? Somehow getting to the South Pacific despite a distinct lack of southerly breezes, the monkey is faced with a problem; he must get his balloon over the Andes Mountains to get, to the Amazon. His hair dryer is already straining to keep the air hot enough to keep him aloft, so he rigs a bellows where he can heat more air to the temperature inside the balloon and then pump it into the balloon. The EPM needs to get his balloon to an altitude of 5000 m, but he can't raise the temperature in the balloon anymore. He can put in more air at the current temperature, thus increasing the balloon's volume.
c) Will this help him? If so, how much air must he pump into the balloon to get over the Andes?