question_answer

A soap bubble in vacuum has a radius 3 cm and another soap bubble in vacuum has radius 4 cm. If two bubbles coalesce under isothermal condition, then the radius of the new bubble will be:

A)  7 cm                     

B)        5 cm                     

C)        4.5 cm                                 

D)  2.3 cm

Correct Answer: B

Solution :

Key Idea: An isothermal process obeys Boyles law. Since process is isothermal the total pressure of air inside the bubble is same as excess of pressure given by \[=\frac{3}{2}\times 0.01\times 100\] where T is surface tension and R is radius . Also an isothermal process obeys Boyles law hence, PV= constant. Let R be the radius of coalesce system then \[=1.5%\] \[Y=3K(1-2\sigma )\]\[{{I}_{1}}\]   \[{{I}_{2}}\] Given, \[\phi \] and \[I={{I}_{1}}+{{I}_{2}}+2\sqrt{{{I}_{1}}{{I}_{2}}}\cos \phi \] \[\cos \phi =-1\]  \[\phi =\pi ,3\pi ,5\pi ,.................\] \[\phi =(2\pi +1)\pi \,n=1,2,3,..............\]