What happens to the air pressure inside a balloon when the balloon is squeezed to half its volume at constant temperature?

Answer 1

Assuming the temperature is constant and none of the air is let out of the balloon, if you half the volume, the air pressure will double.

If you want it, here is the math:

Air is approximately an ideal gas, so when the temperature is constant, it follows the gas law of P1*V1 = P2*V2 where P1 is the pressure at state 1 (i.e. before the balloon is squeezed), V1 is the volume at state 1, P2 is the pressure at state 2 (i.e. after the balloon is squeezed), and V2 is the volume at state 2. When you half the volume, mathematically saying V2 = 0.5*V1. When you substitute this in, your equation now becomes P1*V1 = P2*0.5*V1. The V1 on both sides will cancel, leaving you with P1 = 0.5*P2. Since you are asking about the pressure after you squeeze the balloon, you want to know P2. So if you divide both sides by 0.5, you now have P1/0.5 = P2 or equivalently P2 = 2*P1 and we see that the pressure is twice that of the original.