Question:
A soap bubble of radius $r$ is blown up to form a bubble of radius $2 r$ under isothermal conditions. If $T$ is the surface tension of soap solution, the energy spent in the blowing
A soap bubble of radius $r$ is blown up to form a bubble of radius $2 r$ under isothermal conditions. If $T$ is the surface tension of soap solution, the energy spent in the blowing
Updated On: Sep 3, 2024
- $3 \pi Tr^2 $
- $6 \pi Tr^2 $
- $12 \pi Tr^2 $
- $24 \pi Tr^2 $
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Initially area of soap bubble, $A_1 = 4 \pi r^2$
Under isothermal condition radius becomes 2r.
$\therefore $ Area $A_2 = 4 \pi (2r)^2 = 16 \pi r^2$
Increase in surface area
$\Delta A = 2 (A_2 - A_1 ) $
$= 2(16 \pi r^2 - 4 \pi r^2) $
$= 2 4\pi r^2$
Energy spent,
$W = T \times \Delta A$
$ = T . 24 \pi r^2 $
$= 24 \pi T r^2\, J $
Under isothermal condition radius becomes 2r.
$\therefore $ Area $A_2 = 4 \pi (2r)^2 = 16 \pi r^2$
Increase in surface area
$\Delta A = 2 (A_2 - A_1 ) $
$= 2(16 \pi r^2 - 4 \pi r^2) $
$= 2 4\pi r^2$
Energy spent,
$W = T \times \Delta A$
$ = T . 24 \pi r^2 $
$= 24 \pi T r^2\, J $
Was this answer helpful?
0
1
Top Questions on Surface tension
- A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is 0.07 Nm-1, then the excess force required to take it away from the surface is :
- NEET (UG) - 2024
- Physics
- Surface tension
- A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :
- JEE Main - 2024
- Physics
- Surface tension
- A soap bubble is blown to a diameter of \( 7 \, \text{cm} \). \( 36960 \, \text{erg} \) of work is done in blowing it further. If the surface tension of the soap solution is \( 40 \, \text{dyne/cm} \), then the new radius is ______ \( \text{cm} \). Take: \( \left( \pi = \frac{22}{7} \right) \).
- JEE Main - 2024
- Physics
- Surface tension
- A liquid column of height \(0.04 \, \text{cm}\) balances excess pressure of a soap bubble of certain radius. If density of liquid is \(8 \times 10^3 \, \text{kg m}^{-3}\) and surface tension of soap solution is \(0.28 \, \text{N m}^{-1}\), then diameter of the soap bubble is _________ \(\text{cm}\).
\((\text{if } g = 10 \, \text{m s}^{-2})\)- JEE Main - 2024
- Physics
- Surface tension
- A big drop is formed by coalescing 1000 small identical drops of water. If E1 be the total surface energy of 1000 small drops of water and E2 be the surface energy of single big drop of water, the E1 : E2 is x : 1 where x = ________.
- JEE Main - 2024
- Physics
- Surface tension
View More Questions
Questions Asked in VITEEE exam
- Two identical blocks A and B, each of mass 'm' resting on a smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block 'C' (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is
- VITEEE - 2023
- work, energy and power
- Assertion :
The binding energy of the nucleus increases with the increase in atomic number.
Reason :
Heavier elements have a greater number of non-radioactive isotopes than radioactive isotopes. - The half-life of radioactive radon is 3.8 days. The time at the end of which \(\frac{1}{20}th\) of the Radon sample will remain undecayed is (given log10e=0.4343)
- Which element has more electron gain enthalpy among chalcogen group?
- VITEEE - 2022
- sulphur
- Coin is tossed till heads is obtained what is expectation of no. of coin tosses
- VITEEE - 2022
- Random Variables
View More Questions
Concepts Used:
Surface Tension
The amount of energy required to increase the liquid's surface area by one unit area is known as surface tension. In other words, it is a property of the liquid surface to resist force.
Surface tension is defined as,
The ratio of the surface force F to the length L along which the force acts.
Mathematically, the surface tension formula can be expressed as follows:
T=F/L
Where,
- F is the force per unit length
- L is the length in which force act
- T is the surface tension of the liquid
Read More: Detergents and Surface Tension
Factors affecting surface tension:
- Impurities: The surface tension decreases with the addition of impurities.
- Surfactants: Adding surfactants in liquids lowers the tension of water making it interrupt aside or get susceptible.
- Temperature: The surface tension of a liquid reduces as the temperature rises.
The Unit of Surface Tension:
The SI unit of Surface Tension is Newton per Meter or N/m.