A soap bubble is blown with the help of a mec | vedclass

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

Question

(A) The excess pressure inside a soap bubble is given by $\Delta P = \frac{4T}{r}$,where $T$ is the surface tension and $r$ is the radius of the bubbl

Vedclass · Accepted Answer

Vedclass · Answer

(A) The excess pressure inside a soap bubble is given by $\Delta P = \frac{4T}{r}$,where $T$ is the surface tension and $r$ is the radius of the bubble.
Since the pump increases the volume $V$ of the bubble at a constant rate,we have $\frac{dV}{dt} = k$ (constant).
Integrating this,$V = kt + C$. Assuming the bubble starts from zero volume at $t = 0$,$V = kt$.
Since $V = \frac{4}{3}\pi r^3$,we have $\frac{4}{3}\pi r^3 = kt$,which implies $r = \left(\frac{3kt}{4\pi}\right)^{1/3}$.
Substituting this into the expression for excess pressure: $\Delta P = \frac{4T}{r} = 4T \left(\frac{4\pi}{3kt}\right)^{1/3}$.
Thus,$\Delta P \propto t^{-1/3}$.
The pressure inside the bubble is $P = P_{atm} + \Delta P = P_{atm} + \frac{C'}{t^{1/3}}$,where $C'$ is a constant.
As $t$ increases,$P$ decreases. The graph representing this relationship is a curve that starts from a high value and decreases asymptotically towards $P_{atm}$ as $t$ increases,which corresponds to option $A$.

$A$ soap bubble is blown with the help of a mechanical pump at the mouth of a tube. The pump produces a constant increase per minute in the volume of the bubble,irrespective of its internal pressure. The graph between the pressure inside the soap bubble and time $t$ will be-

Similar Questions

$A$ big liquid drop splits into $n$ similar small drops under isothermal conditions,then in this process

In a cylinder provided with a piston, air is under pressure $P_1$ at a constant temperature $t$. $A$ soap bubble with radius $r$ and surface tension $T$ is lying inside the cylinder. To reduce the radius of the soap bubble to half, the required air pressure inside the cylinder is

Under isothermal conditions, two soap bubbles of radii $a$ and $b$ coalesce to form a single bubble of radius $c$. If the external pressure is $P$, then the surface tension of the bubbles is:

Let $R_1, R_2$ and $R_3$ be the radii of three mercury drops. $A$ big mercury drop is formed from them under isothermal conditions. The radius of the resultant drop is

$A$ vessel having a small hole in the bottom must hold water without leakage when water is poured to a height of $7 \text{ cm}$. What is the radius of the hole (in $\text{ mm}$)? [Surface tension of water is $0.07 \text{ N/m}$, angle of contact is $0^{\circ}$, and $g = 10 \text{ m/s}^2$]

Vedclass Test Series

Exam Paper Generator

Online Exam Module