WILL GIVE BRAINLIEST PLEASE HELP ITS DUE IN 30 MINUTES AND IM REALLY STRESSED enjoy the points :) I have PI in points so I'm giving some away for lucky peeps

Hot air balloons float in the air because of the difference in density between cold and hot air. in this problem, you will estimate the minimum temperature the gas inside the balloon needs to be, for it to take off. to do this, use the following variables and make these assumptions: the combined weight of the pilot basket together with that of the balloon fabric and other equipment is w. the volume of the hot air inside the balloon when it is inflated is v. the absolute temperature of the hot air at the bottom of the balloon is th (where th> tc). the absolute temperature of the cold air outside the balloon is tc and its density is ďc. the balloon is open at the bottom, so that the pressure inside and outside the balloon is the same. as always, treat air as an ideal gas. use g for the magnitude of the acceleration due to gravity.

The atoms of a solid aluminum can are close together, vibrating in a rigid structure. if the can is warmed up on a hot plate, what happens to the atoms?

Some liquids can be distilled, but only at temperatures that are so high that it is impractical, or so high the compound decomposes. explain why distillation such compounds at significantly less than atmospheric pressure (some degree of vacuum) would solve this problem.