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Two identical soap bubbles, each of radi...

Two identical soap bubbles, each of radius .x., coalesce to form a bubble of radius .y., If P be the atmospheric pressure, and assuming that the process is isothermal, what is the surface tension of soap solution ?

Text Solution

Verified by Experts

The correct Answer is:
`T=(P[2x^(3)-y^(3)])/(4(y^(2)-2x^(2)))`
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If two soap bubbles of radii R_(1) and R_(2) (in vacuum) coalasce under isothermal conditions, what is the radius of the new bubble. Take T as the surface tension od soap solution.

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Knowledge Check

  • Under isothermal conditions two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If external pressure is P_O , the surface tension is equal to:

    A
    `( P_O ( a^(3) + b^(3) -c^(3) ) )/( 4 ( a^(2) + b^(2) + c^(2) )`
    B
    `( 4 ( a^(3) + b^(3) - c^(3) ))/( ( a^(2) + b^(2) -c^(2) ) )`
    C
    `(P_0 ( c^(3) - a^(3) - b^(3) ) )/( 4 ( a^(2) + b^(2) - c^(2) ) )`
    D
    `( P( a^(3) + b^(3) - c^(3) ) )/( (a^(2) - b^(2) -c^(2) ) )`

  • Under isothermal conditions two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If external pressure is P_(o) , the surface tension is equal to :

    A
    `(P_(o)(a^(3)+b^(3)-c^(3)))/(4(a^(2)+b^(2)+c^(2)))`
    B
    `(4(a^(3)+b^(3)-c^(3)))/((a^(2)+b^(2)-c^(2)))`
    C
    `(P_(0)(c^(3)-a^(3)-b^(3)))/(4(a^(2)+b^(2)-c^(2)))`
    D
    `(P(a^(3)+b^(3)-c^(3)))/((a^(2)-b^(2)-c^(2)))`

  • Under isothermal conditions two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If external pressure is P_e , the surface tension of soap solution is equal to :

    A
    `(P_e (a^3 +b^3 -c^3 ))/( 4(a^2 +b^2 +c^2))`
    B
    `(4 P_e (a^3 +b^3 -c^3))/( (a^2 +b^2 -c^2 ))`
    C
    `(4 P_e ( c^3-a^3 -b^3 ))/( (a^2 +b^2 -c^3))`
    D
    `(P(a^3 + b^3 -c^3))/((a^2 - b^2 - c^2))`

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