Inflated ball mass? cold air vs worm air?

Question

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 ?

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Answer 1 · 2017-07-16T15:34:12

Inflate with cold air.

You are correct.

We can use the Ideal Gas Law to prove it.

(1) $p V = n R T$ $pV = nRT$

(2) $p = \frac{n R T}{V} = (\frac{n}{V}) R T$ $p = (nRT)/V = (n/V)RT$

But $n = \frac{m}{M}$ $n = m/M$ , so

(3) $p = \frac{m R T}{M V}$ $"p = (mRT)/(MV)$

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.