Gage pressure within a spherical droplet of a fluid is 'p'. What will be gage pressure within a bubble of the same size & of the same fluid ?

ANS:B - 2 p

Let me correct my previous response. When considering the gage pressure within a spherical droplet or bubble, we need to take into account the curvature of the surface. The pressure inside a droplet or bubble is higher than the pressure outside due to the surface tension trying to minimize the surface area. For a spherical droplet or bubble, the gage pressure difference (ΔP) between the inside and outside can be calculated using the Young-Laplace equation: ΔP=r2γ​ Where:

• ΔP is the difference in pressure between the inside and outside of the droplet or bubble.
• γ is the surface tension of the fluid.
• r is the radius of the droplet or bubble.

Given that the size and the fluid are the same for both the droplet and the bubble, the surface tension γ remains constant. However, the curvature of the surfaces differs. For a droplet, the curvature is concave, while for a bubble, the curvature is convex. The radius term in the equation is in the denominator. Since the radius is the same for both the droplet and the bubble, the gage pressure inside the bubble will be higher than that inside the droplet because the curvature term in the denominator is smaller for a bubble due to its convex shape. Therefore, the gage pressure within the bubble of the same size and the same fluid will be twice the gage pressure within the droplet. Hence, the correct answer is 2p.