# When a balloon rises, the outside pressure decreases with altitude, does the pressure inside the balloon decrease accordingly?

When the balloon rises and the pressure on its outer surface decreases, does the inner pressure also decrease? If Boyle's law holds true in this case, then the pressure of the gas inside the balloon decreases since its volume increases. However, were that the case, does the pressure inside equal the pressure outside, i.e., is the gas pressure equal to the atmospheric pressure?

• Why do you think that the pressure inside a rising balloon would be constant? (Hint: the envelope of the balloon is not rigid.) Apr 11 at 10:57
• Mechanical stability (aka Newton's 3rd law) means that the pressure inside the balloon is the same as outside - if this were not the case, the balloon would be changing its shape. Boyle's law also means that the volume of the balloon should increase with lower pressure (if the balloon is closed - this if often not the case for the hot air balloons.) Apr 12 at 7:53

The skin of the balloon behaves, within some reasonable limits, according to Hooke's law: its elongation is proportional to strain. If we denote the tension inside the wall $$\gamma$$, this additional pressure is $$\frac{2\gamma}{r}$$ (from the Young–Laplace equation). Without delving into equations, this can be seen fairly easily: since force scales linearly ($$\propto r$$) and surface area quadratically ($$\propto r^2$$), this extra pressure should scale $$\propto 1/r$$. This is consistent with a common observation: it is difficult to start inflating a balloon, but not so much to add air to an already inflated one.