Why is a soft underinflated football at sea level much firmer when taken to a high elevation in the mountains?

Question

Why is a soft underinflated football at sea level much firmer when taken to a high elevation in the mountains?

Answer 1

PV = nRT

So if we assume temperature didn't change.

You have the same amount of gas in the ball.

So PV = constant

So the volume and internal pressure are inversely proportional.  Less external pressure on the mountain means somewhat less internal pressure, so the ball is bigger.  A fully blown-up ball is harder.

Answer 2

Because the external (atmospheric) pressure on the football is less at higher altitudes.  So long as the amount of air inside the bladder of the football remains the same (from sea level to high altitude), that air will exert more pressure on the bladder when the pressure outside is less, making the bladder firmer.

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Answer 3

The higher the elevation the lower the air pressure is.  So the air inside the football feels less pressure at a higher elevation and can expand out to make the football look more inflated.