# 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 ?

Jul 16, 2017

Inflate with cold air.

#### Explanation:

You are correct.

We can use the Ideal Gas Law to prove it.

(1) $p V = n R T$

(2) $p = \frac{n R T}{V} = \left(\frac{n}{V}\right) R T$

But $n = \frac{m}{M}$, 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.