1. The problem statement, all variables and given/known data We have a chinese lantern (balloon) made of paper, cylinder shaped with the following sizes: base diameter - 45 cm, height - 70 cm. Mass of the balloon is 57 g (21 g from this is mass of "fuel" - the fuel is wax paper!). Fuel is then ignited at the centre of the base, which is open. Therefore the balloon will soar. The question is, how much additional weight can be hung to the balloon and the balloon still takes off. Outside temperature is 5 °C (Let us denote it as cold air). 2. Relevant equations Just see the text. 3. The attempt at a solution First I can compute volume of the balloon, which is of course V = π*r2*h = π*22.52*70 cm3 = 111330.189662 cm3≈0.11133m3. Now the gravitational force of air pressed up by the balloon gives the magnitude of buoyancy: Gcold_air=ρcold_air*V*g = 1.2697*0.11133*g≈1.38723 N. Now we should determine the volume of the fuel, which is Vfuel= mfuel/ρfuel=0.021/650 = 0.00003 m3. Now we will compute Ghot_air=ρhot_air*(V-Vfuel)*g = 1.1277*0.11130*9.871373 ≈ 1.23175 N. Now we can use Archimedes principle: Gcold_air = Ghot_air + m*g + M*g, and we want to solve this equation for M, which is our burden, that can be carried: M = (Gcold_air-Ghot_air-m*g)/g, which gives us M≈-0.04116 kg, which is rubbish... There are just too many determinants, that were omitted: 1) temperature of hot air in the ballon, I chose 40 °C, but how can I know? What if it is 60 °C, then the density would be higher, but how can I know? 2) It would be best if all fuel would just burn out, then the temperature would be the highest and the mass the lowest, so should I wait till the fuel is burn out and only after that I bind the burden? 3) I omitted the air pressed up by the wax paper and the burden. 4) ... inf) There are just too many... I'd be so much grateful for your help!