Two soap bubbles of radii R_(1) and R_(2) kept in atmosphere are combined isothermally to form a big bubble of radius R. The expression for surface tension will be

Two soap bubbles of radii R_(1) and R_(2) kept in atmosphere are combi

1.	Two soap bubbles of radii R_(1) and R_(2) kept in atmosphere are combined isothermally to form a big bubble of radius R. The expression for surface tension will be
Answer» `(P_(0)(R^(3)+R_(1)^(3)+R_(2)^(3)))/(4(R^(2)+R_(1)^(2)+R_(2)^(2)))` `(P_(0)(R_(1)^(3)+R_(2)^(3)-R^(3)))/(4(R^(2)-R_(1)^(2)-R_(2)^(2)))` `P_(0)(R_(1)^(3)+R_(2)^(3)-R^(3))` `4P_(0)(R_(1)^(3)+R_(2)^(3)-R^(3))` Solution :ACCORDING to isothermal process, `PV=P_(1)V_(1)+P_(2)V_(2)` `(P_(o)+(4T)/(R ))(4)/(3)piR^(3)=(P_(o)+(4T)/(R_(1)))(4)/(3)piR_(1)^(3)+(P_(o)+(4T)/(R_(2)))(4)/(3)piR_(2)^(3)` `P_(o)(R^(3)-R_(1)^(3)-R_(2)^(3))=4T(R_(1)^(2)+R_(2)^(2)-R^(2))`