MHT CET · Physics · Mechanical Properties of Fluids

The radius $R$ of the soap bubble is doubled under isothermal condition. If $T$ be the surface tension of the soap bubble, the work done in doing so is given by

A $32 π R^{2} T$
B $24 π R^{2} T$
C $8 π R^{2} T$
D $4 π R^{2} T$

Verified Solution

Answer & Solution

Correct Answer

(B) $24 π R^{2} T$

Step-by-step Solution

Detailed explanation

The surface energy of a bubble

E

= Tension

\times

surface area

E = T \times A

For soap bubble

E = 2 T \times A

E = 2 T \times 4 π R^{2}

Here,

R

= radius of the bubble
If the radius is doubled then we have

E^{'} = 2 T \times 4 π R^{2}

E^{'} = 2 T \times 4 π {(2 R)}^{2}

E^{'} = 32 π R^{2} T

Work done =

E' - E

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The radius R of the soap bubble is doubled under isothermal condition. If T be the surface tension of the soap bubble, the work done in doing so is given by

Step-by-step Solution

The radius $R$ of the soap bubble is doubled under isothermal condition. If $T$ be the surface tension of the soap bubble, the work done in doing so is given by