In hot air balloons the air inside the envelope stays at atmospheric pressure because of the hole in the bottom and the volume of the envelope is essentially constant. Yet in order to raise the balloon it must be heated which increases the its temperature. If the temperature increases how does the pressure and volume stay constant? My guess is that the number of molecules of air in the balloon decreases (decreasing the density). The pressure stays the same because the increased temperature increases the kinetic energy of the remaining molecules. What do you think? I'm not sure if my guess is correct.