Why does a balloon inflate when you blow air into it?

This seems like a common sense question, but are you able to offer a rigorous explanation?

As you try to offer an explanation, you will ask the following: Must the pressure inside the balloon always equal to the pressure outside the balloon?

With more air molecules in the balloon, the pressure inside the balloon increases. The balloon inflates to increase its surface area so that the force acting by the air molecules inside outward = the force acting by the air molecules outside inward.

However, the pressure inside the balloon is generally higher than outside because there are additional tension force pulling against the balloon’s inflation as it stretches outward.

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