Physics 103: Kinetic Theory and Elasticity

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Questions and Answers

What is the size of a molecule of a gas?

2 x 10^-10 m

What is the order of the distance between gas molecules?

2 x 10^-9 m

Who developed the Kinetic Theory of Gases?

Rudolph Clausius and James Clark Maxwell

What are the assumptions of the Kinetic Theory of Gases regarding the motion of molecules and the nature of gases?

<p>All gases consist of molecules. (A), The molecules of a gas are very small in size compared to the distance between them. (B), The molecules of a gas are always in random motion. (C), The molecules of a gas behave as perfect elastic spheres. (D)</p> Signup and view all the answers

What happens when gas molecules collide with each other or with the walls of the container?

<p>Gas molecules experience changes in their velocities.</p> Signup and view all the answers

What is the term used to describe the distance covered by a molecule between two successive collisions?

<p>Free path</p> Signup and view all the answers

Collisions between molecules of a gas are nearly instantaneous.

<p>True (A)</p> Signup and view all the answers

Gas molecules exert forces on each other only during collisions.

<p>True (A)</p> Signup and view all the answers

What is the pressure exerted by a gas on the walls of the container caused by?

<p>Continuous collisions of the gas molecules against the walls of the container</p> Signup and view all the answers

What is the formula used to calculate the mean square velocity along the three axes, x, y, and z?

<p>√(Vx^2 + Vy^2 + Vz^2)</p> Signup and view all the answers

Define density of a gas.

<p>The mass of the gas per unit volume.</p> Signup and view all the answers

What is the formula for the kinetic energy of a gas molecule?

<p>1/2 * m * v^2</p> Signup and view all the answers

What is the formula for the pressure of a gas given the kinetic energy of the gas molecules and the number of molecules per unit volume?

<p>P = 1/3 * N * (1/2 * m * V^2)</p> Signup and view all the answers

What is the formula for the pressure of a gas given the total number of gas molecules, the density of the gas, and the mean square velocity of the gas molecules?

<p>P = 1/3 * (m * n * v^2)</p> Signup and view all the answers

What is the formula for the average kinetic energy of a mole of gas?

<p>1/2 * M * V^2 = RT</p> Signup and view all the answers

What is the formula for the average kinetic energy of a single gas molecule?

<p>1/2 * m * V^2 = 3/2 * k*T</p> Signup and view all the answers

Define mean velocity of gas molecules.

<p>Mean velocity is the arithmetic mean of the velocities of all the gas molecules.</p> Signup and view all the answers

Define root-mean-square (RMS) velocity of gas molecules.

<p>RMS velocity is the square root of the average of the squares of the velocities of all gas molecules.</p> Signup and view all the answers

What is the defining characteristic of an elastic body?

<p>An elastic body returns to its original shape and size when the deforming force is removed.</p> Signup and view all the answers

What is Hooke's Law?

<p>Hooke's Law states that the extension produced in a wire is directly proportional to the load attached to it.</p> Signup and view all the answers

What is stress?

<p>Stress is defined as the restoring force per unit area set up in a body when deformed by an external force.</p> Signup and view all the answers

What are the two types of stress?

<p>Normal stress and tangential stress.</p> Signup and view all the answers

What is Young's Modulus?

<p>Young's Modulus is defined as the ratio of normal stress to longitudinal strain.</p> Signup and view all the answers

What is bulk modulus?

<p>Bulk modulus is defined as the ratio of normal stress to volumetric strain.</p> Signup and view all the answers

What is compressibility?

<p>Compressibility is the reciprocal of bulk modulus.</p> Signup and view all the answers

Flashcards

Kinetic Theory of Gases

A theory explaining gas laws through molecular motion.

Mean Free Path

Average distance a gas molecule travels between collisions.

Pressure

Force exerted by gas molecules against container walls.

Ideal Gas Equation

Relationship between pressure, volume, and temperature: PV = RT.

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Elasticity

Property of material to return to original shape after deformation.

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Hooke's Law

Extension in a wire is proportional to the load applied.

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Stress

Restoring force per unit area when a body is deformed.

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Strain

The ratio of change in dimension to original dimension.

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Young's Modulus

Ratio of normal stress to longitudinal strain.

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Bulk Modulus

Ratio of normal stress to volumetric strain.

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Compressibility

Reciprocal of bulk modulus; measure of how much a material can compress.

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Shear Modulus

Ratio of tangential stress to shear strain.

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Mean Velocity of Gas Molecules

Average velocity of a gas molecule.

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Root Mean Square Velocity (vrms)

Square root of the average of the squares of molecular speeds.

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Elastic Limit

Maximum stress a material can withstand while returning to original shape.

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Tensile Stress

Deforming force acting per unit area, normal to the surface.

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Volumetric Strain

Change in volume per unit original volume when deformed.

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Shear Strain

The change in shape of a body when subjected to shear stress.

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Collisions per Second

The number of times a molecule hits another or the walls in a second.

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Density (ρ)

Mass per unit volume of a substance.

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Elastic Body

A body that returns to its original shape after deformation within elastic limits.

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Plastic Body

A body that does not return to its original shape after deformation.

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Normal Stress

Force acting per unit area, normal to the surface.

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Tangential Stress

Force acting per unit area parallel to the surface.

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Modulus of Elasticity

Constant that indicates the elastic response of a material.

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Coefficient of Restitution

Ratio that measures the elasticity of collisions.

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Intermolecular Forces

Forces acting between molecules.

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Random Motion

Movement in any direction at any speed.

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Elastic Potential Energy

Energy stored in a body due to deformation.

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Study Notes

Physics 103: General Physics III

  • Course: General Physics III (Behavior of Matter)
  • Semester: First Semester 2025
  • Lecturer: Prof. Tajudeen O. Ahmed
  • Date: January 22nd, 2025

Course Outline

  • Kinetic Theory of Gases:

    • Molecular collisions and mean free path

  • Elasticity:

    • Hooke's Law
    • Young's modulus
    • Shear modulus
    • Bulk modulus
  • Advanced Level Physics by Nelkon & Parker
  • College Physics by Frederick J. Bueche & Eugene Hecht

Kinetic Theory of Gases (Page 2)

  • Gases are collections of many molecules in continuous motion.
  • Molecular size is approximately 2 x 10⁻¹⁰ m.
  • Distance between molecules is about 10 times their size.
  • Molecules move freely except during collisions.
  • Molecular collisions cause changes in velocities.
  • Kinetic theory explains gas laws based on molecular motion.
  • Assumptions about ideal gas motion are made.

Pressure Exerted by a Gas (Page 3)

  • Gas molecules collide with container walls, exerting pressure.
  • Pressure results from continuous molecular collisions.
  • Pressure is calculated using molecular velocities and number density.
  • Calculations include components of molecular velocity along x, y, and z axes.

Kinetic Energy (Page 4, 5, 6)

  • The average kinetic energy of gas molecules is calculated.
  • Average kinetic energy is proportional to temperature (T).
  • The formula PV = nRT shows the relationship between pressure, volume, and temperature.
  • KINETIC ENERGY of a molecule and ONE MOLE OF A GAS Formula is provided.

Mean Velocity of Gas Molecules (Page 7)

  • Mean velocity is the average speed of gas molecules.
  • The formula for the root mean square (rms) velocity is provided.

Root Mean Square Velocity (Page 8)

  • The root mean square velocity formula is given; and examples to compute kinetic energy of a gas, and mean velocity of a gas.

Mean Free Path (Pages 9, 10)

  • Mean free path is the average distance a molecule travels between collisions.
  • The mean free path is related to molecular size, density, and temperature.
  • It is calculated using molecular diameter and number density.
  • Formula for mean free path is given.

Elasticity (Page 12)

  • Elasticity is a material property where, after a deforming force is removed, the material returns to its original shape and size.
  • Hooke's Law states that extension is proportional to load for small extensions.
  • Hooke's Law defines the limit within which a material is elastic.

Stress (Page 13)

  • Stress is the restoring force per unit area within a material when a deforming force is applied.
  • Stress is calculated as the force divided by the area.

Strain (Page 14)

  • Strain is the ratio of change in length to the original length.

Young's Modulus (Page 15)

  • Young's modulus is the ratio of stress to strain for a material under tensile or compressive stress.
  • Formula for Young's Modulus is provided.

Stress versus Strain (Page 16)

  • Graph showing stress versus strain.
  • The graph's regions are defined: proportional limit, elastic limit, yield point, and breaking point.

Bulk Modulus (Page 17)

  • Bulk modulus is the ratio of stress to volumetric strain.
  • Formula is given to calculate bulk modulus.

Compressibility (Page 18)

  • Compressibility is the reciprocal of bulk modulus.
  • Formula for Compressibility is provided and examples are given.

Shear Modulus (Page 19)

  • Shear Modulus is the ratio of shearing stress to shearing strain
  • Formula for shear modulus is given

Additional Notes (Page 20)

  • Calculations for shearing strain, shearing stress, and shearing force are shown in the example provided.

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