Question

216 small identical liquid drops each of surface area \( A \) coalesce to form a bigger drop. If the surface tension of the liquid is \( T \), the energy released in the process is

• A. \( 360 AT \)
• B. \( 180 AT \)
• C. \( 90 AT \)
• D. \( 120 AT \)

Hint:

When small drops merge, volume is conserved, but surface area decreases, leading to energy release.

Answer 1

The Correct Option is B

Total surface energy before merging: \[ E_{\text{initial}} = 216 \times T \times A \] After merging, volume remains constant: \[ \frac{4}{3} \pi r^3 = 216 \times \frac{4}{3} \pi r_0^3 \] \[ r = 6 r_0 \] New surface area: \[ A_{\text{new}} = 4\pi (6r_0)^2 = 36 \times 4\pi r_0^2 = 36 A_0 \] Final energy: \[ E_{\text{final}} = 36 T A \] Energy released: \[ \Delta E = 216 TA - 36 TA = 180 TA \] Thus, the energy released is \( 180 AT \).