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Inflated ball mass? cold air vs worm air?

Does it matters to the ball's mass how we inflate it to it's maximum, with cold or worm air?cold air is denser ?

Answer 1

Caleb Adams

Inflate with cold air.

You are correct.

We can use the Ideal Gas Law to prove it.

(1) #pV = nRT#

(2) #p = (nRT)/V = (n/V)RT#

But #n = m/M#, so

(3) #"p = (mRT)/(MV)#

Also, #m/V = ρ#, so

(4) #p = (ρRT)/M# or

#color(blue)(bar(ul(|color(white)(a/a)ρ = (pM)/(RT)color(white)(a/a)|)))" "#

This shows that density is inversely proportional to the Kelvin temperature.

Thus, you can add a greater mass of air at a lower temperature.

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Answer 2

Caleb Adams

The mass of an inflated ball remains constant regardless of whether it is filled with cold air or warm air. However, the density of the air inside the ball will change with temperature, affecting its pressure and thus its bounce characteristics.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.