Calculate how high balloon rises before stopping

1. The problem statement, all variables and given/known data



A Mylar balloon is filled with helium to a pressure just greater than 1.00 atm on a day when the temperature is 30°C. It is released near sea level (an altitude of 0.00 meters). Using the Standard Altitude/Density Table below, estimate the maximum altitude reached by the balloon.



Assume that the Mylar is very thin, very strong, and completely inelastic. Assume further that the radius of the balloon is very large. The balloon does not pop when rising.



The mass density of helium at 1.00 atm and 30°C is 0.180 kg/m³.









2. Relevant equations



I may be wrong about these but this is what I believe is relevant so far:



P = Force/Area = pgh





3. The attempt at a solution



We haven't reached this in lecture yet but I am just studying ahead.



When the balloon comes to a stop, its weight will equal the atmospheric pressure.



P_atm = mg

P = pgh = mg

p is the atmospheric density

ph = m

h = mass of helium / density of air at that height



I don't have a specific volume to use to solve for mass of helium and density of air changes at different altitudes so I don't think this is the right course for this problem.



Using the chart I match the standard density with helium density. The altitude is inbetween 14000 and 16000 and pressure inbetween 140 and 100 (x100Pa).



It looks like .18 kg/m^3 match up with just over 1 atm in the chart. I'm wondering if the temperature has any effect on the balloon. I mean, temperature changes the higher you go and from my limited knowledge, I don't think it has an effect.



Please don't solve it for me as I'd like to figure this out on my own. I'm just having trouble finding relevant equations for this problem or something...