Thermodynamics mass and energy analysis Problem

[boyongo]

Im doing a balloon problem. The problem states that the volume increases linearly with pressure in the solution manual they that P2/P1=V2/V1 i think that is related linearly but i cant figure how. Can some explain?

 

[gneill]

When you write an equation like
$$\frac{V2}{V1} = \frac{P2}{P1}$$
It's usually because there's a linear relationship like
$$P = k V$$
that underlies it, where k is some constant of proportionality. When you "stack" the equation, the proportionality constant drops out:
$$\frac{\rlap{\backslash} k V2}{\rlap{\backslash} k V1} = \frac{P2}{P1}$$

 

[boyongo]

thank you very much :)