Constant Temperature Bubble Expansion: Work Calculation for Changing Radius

[Grand]

Homework Statement

A soap bubble of radius $$R_1$$ and surface tension $$\gamma$$ is expanded at constant temperature by forcing in air by driving in fully a piston containing volume $$v$$. We have to show that the work needed to increase the bubble's radius to $$R_2$$ is:

$$\Delta W=P_2V_2ln\frac{P_2}{P_1} + ...$$

I know hoow to work out the dots (due to surface tension and work against the atmosphere. But for the first term I need to work out the integral:

$$\int_{V_1+v}^{V_2} PdV$$
which I don't really know how to do. If I apply the ideal gas law, I pick a minus sign on the way.

 

[tiny-tim]

Hi Grand!

(write "itex" rather than "tex", and it won't keep starting a new line )

ln(P₂/P₁) = - ln(V₂/V₁) … does that help?

if not, show us what you got ​