Constant Temperature Bubble Expansion: Work Calculation for Changing Radius

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The discussion focuses on calculating the work required to expand a soap bubble from radius R_1 to R_2 at constant temperature. The key equation involves the integral of pressure over volume, specifically ∫PdV, which the user is struggling to compute. They mention using the ideal gas law but encounter issues with signs in their calculations. Additionally, a relationship between pressure and volume is noted, suggesting ln(P2/P1) = -ln(V2/V1). The conversation encourages further sharing of calculations to clarify the work needed against surface tension and atmospheric pressure.
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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.
 
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Hi Grand! :smile:

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

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

if not, show us what you got :smile:​
 
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