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In an isothermal process, two soap bubble of radius a and b combine and form a bubble of radius c. If the external pressure is p, then prove that the surface tension of the soap solution is T-(p(c^3-a^3-b^3))/(4(a^2+b^2-c^2)).

Answer» <html><body><p></p>Solution :We know , the <a href="https://interviewquestions.tuteehub.com/tag/excess-978535" style="font-weight:bold;" target="_blank" title="Click to know more about EXCESS">EXCESS</a> pressure inside the soap <a href="https://interviewquestions.tuteehub.com/tag/bubble-904920" style="font-weight:bold;" target="_blank" title="Click to know more about BUBBLE">BUBBLE</a> = internal pressure - external pressure. <br/> `<a href="https://interviewquestions.tuteehub.com/tag/therefore-706901" style="font-weight:bold;" target="_blank" title="Click to know more about THEREFORE">THEREFORE</a>`For the bubble of radius a, excess pressure, <br/> `(<a href="https://interviewquestions.tuteehub.com/tag/4t-319060" style="font-weight:bold;" target="_blank" title="Click to know more about 4T">4T</a>)/(a)=p_a-p` <br/> `therefore p_a=(p+(4T)/(a))` <br/> Similarly, for the bubble of radius b, <br/> `p_b=(p+(4T)/(b))` <br/> For the bubble of radius c, <br/> `p_c=(p+(4T)/(c ))` <br/> Boyle.s law is applicable in isothermal process. According to this law. <br/> `p_a V_a+p_b V_b=p_c V_c` <br/> or, `(p+(4T)/(a))xx(4)/(3)pia^3+(p+(4T)/(b))xx(4)/(3)pib^3` <br/> `=(p+(4T)/(c ))xx(4)/(3)pic^3` <br/> or, `(p+(4T)/(a))a^3+(p+(4T)/(b))b^3=(p+(4T)/(c ))c^3` <br/> or, `4T(a^2+b^2-c^2)=p(c^3-a^3-b^3)` <br/> `therefore T=(p(c^3-a^3-b^3))/(4(a^2+b^2-c^2))`.</body></html>


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