A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be :
(Given \(\pi\) = 3.14)
(Given \(\pi\) = 3.14)
\(8.5 × 10^{–4} J\)
\(8.2 × 10^{–4} J\)
\(7.5 × 10^{–4} J\)
\(5.3 × 10^{–4} J\)
The Correct Option is C
Solution and Explanation
\(729×\frac 43\pi r^3=\frac 43\pi R^3\)
\(R = 9r\) ……(1)
Then, the gain in surface energy
\(ΔU = S × ΔA\) …..(2)
\(△U=S×{−4\pi R^2+729×4\pi r^2}\)
\(△U=S×4π(729r^2–81r^2)\)
\(△U=7.5×10^{−4}J\)
So, the correct option is (C): \(7.5 × 10^{–4} J\)
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Concepts Used:
Kinetic Theory
The kinetic theory is a fundamental concept in physics and chemistry that describes the behavior of gases, liquids, and solids in terms of the motion of their constituent particles. According to the kinetic theory, all matter is made up of tiny particles, such as atoms or molecules, that are constantly in motion.
The kinetic theory postulates that the temperature of a substance is directly proportional to the average kinetic energy of its particles. The higher the temperature, the greater the motion of the particles, and the more energy they possess.
In a gas, the kinetic theory explains that the particles move randomly and independently, colliding with one another and with the walls of their container. These collisions are elastic which means that no energy has lost during the collision. As a result, the pressure of the gas is directly related to the average speed of its particles and the number of collisions per unit area.
In a liquid or a solid, the particles are more closely packed and have less freedom of motion than in a gas. However, they still vibrate and move, and the kinetic theory explains their behavior in terms of the strength of their intermolecular forces and the amount of energy they possess.
Overall, the kinetic theory provides a framework for understanding the behavior of matter at the atomic and molecular level and has many practical applications, such as in the design of engines, the production of gases, and the study of the properties of materials.