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 ?

1 Answer
Jul 16, 2017

Answer:

Inflate with cold air.

Explanation:

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.