Question:medium

Calculate the vapour pressure that can help the formation of a spherical droplet of water of radius $25 \times 10^{-5}\text{ m}$ at $22^\circ\text{C}$. Given: The surface tension of water at the given temperature is $28 \times 10^{-2}\text{ N m}^{-1}$.

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Be very careful when reading the question context. A water droplet has only $1$ free surface layer, so $\Delta P = \frac{2T}{r}$. If it were a soap bubble suspended in air, it would have $2$ free surfaces, changing the formula to $\Delta P = \frac{4T}{r}$.
Updated On: May 20, 2026
  • $8.81 \times 10^{3}\text{ Pa}$
  • $2.33 \times 10^{3}\text{ Pa}$
  • $6.64 \times 10^{4}\text{ Pa}$
  • $1.01 \times 10^{5}\text{ Pa}$
Show Solution

The Correct Option is B

Solution and Explanation

Understanding the Concept: For a spherical liquid droplet to form or stay stable, the pressure inside the droplet must exceed the pressure outside. This difference is known as excess pressure ($\Delta P$). For a spherical droplet with a single surface boundary layer, the excess pressure is calculated as: \[ \Delta P = \frac{2T}{r} \] where $T$ represents the surface tension and $r$ is the radius of the droplet.
Step 1: Substitute values to calculate excess pressure ($\Delta P$).
Given values:
Surface tension, $T = 7.28 \times 10^{-2}\text{ N m}^{-1}$
Radius, $r = 6.25 \times 10^{-5}\text{ m}$
Let's compute the value of $\Delta P$: \[ \Delta P = \frac{2 \times 7.28 \times 10^{-2}}{6.25 \times 10^{-5}} \] \[ \Delta P = \frac{14.56 \times 10^{-2}}{6.25 \times 10^{-5}} = \frac{14.56}{6.25} \times 10^3 \] \[ \Delta P = 2.3296 \times 10^3\text{ Pa} \approx 2.33 \times 10^3\text{ Pa} \]
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