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91Ó°ÊÓ

In a gas sample, consider a collision between two gas molecules simuluncously, which of the following is correct? (a) Total K.E. of gas molecules increases (b) Total K.E. of gas molecules decreases (c) Total momenum decrcases (d) K.E of first molecule may increase and K.E. of second molecule may decrease

Short Answer

Expert verified
Correct answer: (d) K.E of first molecule may increase and K.E. of second may decrease.

Step by step solution

01

Understand the Problem

We have a collision between two gas molecules and need to determine what happens to their kinetic energy (K.E.) and momentum. We're given four options to consider: increase, decrease, conservation of momentum, and the change in individual K.E.
02

Conservation of Momentum

In a collision, especially an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. Therefore, the total momentum of the gas molecules remains constant; it does not decrease.
03

Conservation of Kinetic Energy

In elastic collisions, the total kinetic energy of the system is conserved. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Hence, it does not increase or decrease.
04

Evaluate Individual Kinetic Energies

Even though the total kinetic energy remains constant, the kinetic energies of individual molecules can change. This means that one molecule can lose kinetic energy while another gains, satisfying energy conservation.
05

Conclusion

Given the analysis, we conclude that during the collision between two gas molecules, it is possible for the kinetic energy of one molecule to increase while the other decreases, without affecting the total kinetic energy of the system.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Kinetic Energy Conservation
In physics, kinetic energy conservation is an essential concept when analyzing elastic collisions. During an elastic collision, like the interactions between gas molecules, the total kinetic energy remains unchanged. This means the kinetic energy before the collision is equal to the kinetic energy after the collision. Why is this important? Because it helps to predict the outcome of molecular interactions. Notably, while the total kinetic energy is stable, individual molecules might experience changes in their kinetic energy. This can occur with one molecule gaining energy as another loses it, balancing out any alterations.
Momentum Conservation
Momentum conservation is fundamental when examining collisions, especially among gas molecules. Imagine two molecules colliding in a gas. No matter how chaotic the interaction may seem, the total momentum of the system remains constant if no external forces intervene. Total momentum before equals total momentum after. This concept ensures predictability in physics: by knowing initial conditions, outcomes can be calculated. It's crucial because momentum conservation helps explain how molecules behave after they collide, forming the basis for understanding molecular dynamics in gases.
Molecular Collisions
Molecular collisions are interactions between molecules that involve exchange and transfer of energy. In gases, these collisions are frequent due to rapid molecular motion. Two types of collisions are common: elastic and inelastic. In elastic collisions, both kinetic energy and momentum are conserved. This means the molecules bounce off each other without losing energy to other forms, like heat or deformation. On the other hand, in inelastic collisions, kinetic energy isn't fully conserved as some transform into other forms of energy. Understanding these concepts helps delineate the behavior of substances in different states and conditions.
Gas Molecules
Gas molecules constantly move and collide, creating dynamic and constantly changing environments. They move at high speeds and travel in straight lines until they collide with other molecules or obstacles. Each collision can result in changes of directions and speeds, all while obeying the principles of conservation of momentum and energy in the case of elastic collisions. The behavior of gas molecules under these conditions explains phenomena like pressure and temperature in gases. The more gas molecules present, the higher the chance of collisions, leading to increased pressure. This makes understanding molecular behavior vital in fields such as thermodynamics and fluid dynamics.

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Most popular questions from this chapter

The encrgy of gas molecules in a gas al given lemperature \(T(K)\) is calculated based on kinctic theory of gascs. Column-I Column-II (a) Mean kinetic energy per mole of diatomic gas (p) \((f / 2) K T\) (b) Mean kinetic energy per molecule of gas (q) \((3 / 2) R T\) (c) Mean kinetic energy per mole of an ideal gas (r) \((5 / 2) R T\) (d) Mean kinetic energy per molecule of poly atomic gas (s) \((7 / 2) K T\)

Which of the following statements is not correct for an ideal gas? (a) Internal energy of an ideal gus does not depend on its volume. (b) Specific heat of any ideal gas is equal to \(\frac{3}{2} R\). (c) If any gas obeys Boyle's law, Charle's law, then it must always be an ideal gas. (d) Ideal gas molecules have finite mass and so small volume.

Match the following two columns for 2 moles of a diatemic gas at room temperature \(T\). Column-I Column-II (a) Translational kinetic energy (p) \(2 R T\) (b) Rotational kinctic energy (q) \(4 R T\) (c) Potential chergy (r) \(3 R T\) (d) Total internal cnergy (s) None

The temperature \(T\) is measured by a constant volume gas thermometer (a) \(T\) is independent of the gas used at high pressure (b) \(T\) is independent of the gas used at low prossure (c) The ideal gas scale agrec with the absolute scale of temperature (d) The ideal gas scale does not agree with the absolute scale

Find cquation of polytropic process for which heat capacity is \(C=(7 / 2) R\) for a monoatomic gas. (a) \(P V=\) constant (b) \(P V^{2}=\) constant (c) \(P^{2} V=\) constant (d) None

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