homework and exercises - Will there be buoyancy in a space with atmospheric pressure and no gravity?

If there is pressure but not gravity will there be buoyancy? For example on an inertial spacecraft.

I guess there will be no buoyancy, because there will be no direction of buoyancy without gravity.

Answer

The buoyant force is $\rho V g$ so if $g=0$ then the force is zero also. However, I would like to comment on your argument:

I guess there will be no buoyancy, because there will be no direction of buoyancy without gravity.

This is called an argument by symmetry, and it is a very powerful method for argument. Since the buoyant force always points “up” and there is no up direction in space, which way could it point? Therefore it must be zero since any other force vector would single out an up direction. I encourage you to make symmetry arguments as often as possible.