Balloons

Let us look at balloons. Since in natural circumstances they are fully immersed in the air, we conclude that whether they will sink, remain floating, or move upwards, depends on whether the ballons density is greater than, equal to, or less than, that of the surrounding air. If the balloon is filled with air, then it will sink in air because its average density includes the density of the balloon's material (say rubber for small ones, silk or nylon for larger ones). Thus the ballon must be filled with a gas such as Helium which is less dense than air. The density of air near the surface of the Earth is about $1.25 kg/m^3$ while that of Helium is $0.14$ of that value. Thus a Helium filled balloon will move upwards when released. But even theoretically, the balloon cannot keep going up forever. The reason is that density of air decreases as we go upwards, as those of you who have gone mountain climbing know. Why is this so? Well, just think of our atmosphere: It is mainly concentrated in a belt of 6km in thickness, held there by the force of gravity. But why doesn't gravity pull all the air down to the ground? Actually it tries to, but as more of the air is pulled down, the pressure and density at ground level builds up which creates an opposing upwards force. Thus in equilibrium in the atmosphere reaches a density profile which is approximately exponentially decreasing with height. Thus the buoyancy force on a balloon decreases with height. For hot-air balloons as discussed below, this sets a limit to how high a baloon can go. For gas-filled balloons, such as those used to gather wind speed and direction data, the skin will rupture when it has expanded sufficiently at large heights. The pressure due to air at ground level is about $100,000 N/m^2$ (or ``Pa" after Pascal). This large pressure acts on our bodies but we do not realise it because our bodies produce balancing internal forces. Only when there is an imbalance, such as when we climb a mountain or are in a plane, that we notice some discomfort. Hydrogen as a balloon gas is cheaper and more abundant than Helium, but is also flammable and so can be dangerous. Note that though hydrogen is half as dense as helium, its lifting capacity is only slightly better than that of helium.