A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :
- P
- 8P
- 32P
- 64P
The Correct Option is C
Solution and Explanation
We know that,
\(PV^γ\) = Constant
\(PV^γ=(P')(\frac v8)^γ\)
Where,
\(γ=\frac 53\)
\(P'=32P\)
So, the correct option is (C): \(32P\)
Top Questions on kinetic theory
- Mean free path is inversely proportional to (n = number density, d = diameter of particle)
- KEAM - 2025
- Physics
- kinetic theory
- The equation for the RMS velocity is given as \[ v_{\text{rms}} = \sqrt{\frac{3RT}{M_0}} \] where \( R \) is the gas constant, \( T \) is the temperature, and \( M_0 \) is the molecular mass. If the temperature is increased, find the new RMS velocity \( v_{\text{rms}} \) when the temperature is doubled.}
- MHT CET - 2025
- Physics
- kinetic theory
The motion of a particle in the XY plane is given by \( x(t) = 25 + 6t^2 \, \text{m} \); \( y(t) = -50 - 20t + 8t^2 \, \text{m} \). The magnitude of the initial velocity of the particle, \( v_0 \), is given by:
- OJEE - 2024
- Physics
- kinetic theory
- A body of mass \( m \) moves along the X-axis such that at time \( t \), its position is \( x(t) = \alpha t^4 - \beta t^3 + \gamma t \), where \( \alpha \), \( \beta \), and \( \gamma \) are constants. The acceleration of the body is:
- OJEE - 2024
- Physics
- kinetic theory
- A stone is dropped from the top of a tower. The height through which it falls in the first 3 seconds of its motion equals the height through which it falls in the last second of its motion. To reach the ground, the stone takes time equal to (g = 10 m/s\(^2\)):
- OJEE - 2024
- Physics
- kinetic theory
Questions Asked in JEE Main exam
- The value of \( (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) \) is:
- JEE Main - 2025
- Trigonometric Identities
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
Let \( A = \{-3, -2, -1, 0, 1, 2, 3\} \). A relation \( R \) is defined such that \( xRy \) if \( y = \max(x, 1) \). The number of elements required to make it reflexive is \( l \), the number of elements required to make it symmetric is \( m \), and the number of elements in the relation \( R \) is \( n \). Then the value of \( l + m + n \) is equal to:
- JEE Main - 2025
- Sets and Relations
For hydrogen-like species, which of the following graphs provides the most appropriate representation of \( E \) vs \( Z \) plot for a constant \( n \)?
[E : Energy of the stationary state, Z : atomic number, n = principal quantum number]- JEE Main - 2025
- Hydrogen
- Concentrated nitric acid is labelled as 75%by mass. The volume in mL of the solution which contains 30 g of nitric acid is: Given: Density of nitric acid solution is 1.25 g/mL.
- JEE Main - 2025
- Solutions
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.