# Does the amount/speed a balloon rises vary with the temperature of the gas inside, given a constant type and amount of gas?

I'm attempting to conduct an experiment with a balloon. I fill it up with some amount of helium. If I cool the balloon down (say with liquid nitrogen), the balloon's volume will decrease (because of Charles' Law), and if I heat it up, the balloon will expand. Does this expansion and contraction of the balloon mean that it will float more or less? Or does the amount it float just correspond to the mass of the gas contained in the balloon (in this case constant)?

• Do you know the formula for the buoyant force on an object immersed in a fluid? – The Photon Dec 19 '18 at 21:42
• Is air a fluid? – Raymo111 Dec 19 '18 at 22:11
• Yes, liquids and gasses are two kinds of fluids. – The Photon Dec 19 '18 at 22:12
• No I don't know the formula, what is it? – Raymo111 Dec 19 '18 at 22:14

$$F_B = \rho V g$$
where $$\rho$$ is the density of the fluid, $$V$$ is the volume displaced by the object (the volume of the object itself, if it's fully immersed), and $$g$$ is the acceleration due to gravity.
So in your scenario, you will decrease and increase $$V$$ as you cool and heat the balloon, and thus decrease and increase the buoyant force, changing the acceleration of the balloon. You could even create a scenario where the balloon falls downward when cooled but ascends when heated.