Work both problems. Both problems have equal weight. A hot air balloon initially contains air at 100 kPa and 37C in a volume of 525 m 3 . In order to increase its elevation to the desired height the temperature of the air in the balloon must be increased to 47C. Using a butane burner atmospheric air is heated to 67C and added to the balloon. The balloon may be taken as adiabatic and its skin is deformable, so that it stays at the ambient pressure of 100 kPa.
Italicized values are from air table or ideal gas equation.
Bold values are calculated. Next we calculate our initial mass from the ideal gas law. The human body may be considered a heat engine. A world class sprinter may be considered a most efficient heat engine. Consider that the work output of the sprinter is the kinetic energy change that occurs during a 100 m sprint.