A soap bubble of radius r is blown up to from a bubble of radius 2r under isothermal conditions. If T is the surface tension of soap solution, the energy spent in the blowing :
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Initial surface area of soap bubble = 4πr²
final surface area of soap bubble = 4π(2r)² = 16πr²
∴ inicrease in surface area of soap bubble = (16πr² - 4πr²) = 12πr²
∵ a bubble has two surfaces,
∴ total increases surface area of a soap bubble = 2 × 12πr² =24πr²
Now, energy spent in the blowing = surface tension × increases surface area
= T × 24πr²
= 24πr²T
Hence, answer is 24πr²T
final surface area of soap bubble = 4π(2r)² = 16πr²
∴ inicrease in surface area of soap bubble = (16πr² - 4πr²) = 12πr²
∵ a bubble has two surfaces,
∴ total increases surface area of a soap bubble = 2 × 12πr² =24πr²
Now, energy spent in the blowing = surface tension × increases surface area
= T × 24πr²
= 24πr²T
Hence, answer is 24πr²T
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