The change in surface energy when a big spher | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The volume of the big drop is equal to the total volume of $n$ small droplets: $\frac{4}{3} \pi R^3 = n 	imes \frac{4}{3} \pi r^3$. From this, we

Vedclass · Accepted Answer

$4 \pi R^2(n^{1/3}-1) T$

Vedclass · Answer

(B) The volume of the big drop is equal to the total volume of $n$ small droplets: $\frac{4}{3} \pi R^3 = n 	imes \frac{4}{3} \pi r^3$. From this, we get $r^3 = \frac{R^3}{n}$, which implies $r = \frac{R}{n^{1/3}}$. The surface area of the big drop is $A = 4 \pi R^2$. The total surface area of $n$ small droplets is $A' = n 	imes 4 \pi r^2$. Substituting $r = R n^{-1/3}$, we get $A' = n 	imes 4 \pi (R n^{-1/3})^2 = n 	imes 4 \pi R^2 n^{-2/3} = 4 \pi R^2 n^{1/3}$. The change in surface area is $\Delta A = A' - A = 4 \pi R^2 n^{1/3} - 4 \pi R^2 = 4 \pi R^2 (n^{1/3} - 1)$. The change in surface energy is $\Delta U = T 	imes \Delta A = 4 \pi R^2 (n^{1/3} - 1) T$.

The change in surface energy when a big spherical drop of radius $R$ is split into $n$ spherical droplets of radius $r$ is ($T=$ surface tension).

Similar Questions

The amount of energy required to form a soap bubble of radius $2\,cm$ from a soap solution is nearly $..........\,\times 10^{-4}\,J$: (surface tension of soap solution $=0.03\,N\,m^{-1}$)

Work done in increasing the size of a soap bubble from a radius of $3 \ cm$ to $5 \ cm$ in millijoules is nearly (surface tension of soap solution $= 0.03 \ Nm^{-1}$) (in $\pi$)

$A$ soap bubble of radius $R$ is blown. After heating the solution, a second bubble of radius $2R$ is blown. The work required to blow the second bubble in comparison to that required for the first bubble is

The surface tension of a liquid is $0.5 \, N/m$. If a film is held on a ring of area $0.02 \, m^2$,its surface energy is:

The surface tension of a liquid is $5 \,N/m$. If a film is held on a ring of area $0.02 \,m^2$,its surface energy is about ........... $J$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module