Thermal Physics Notes

Thermal Physics - Topic 2

Kinetic Particle Model of Matter

  • States of matter: Solid, Liquid, Gas

  • Particle model

  • Gases and the absolute scale of temperature

2.1.1 States of Matter

  • Three states of matter: Solid, Liquid, Gas

Characteristics of Each State:

  • Solid

    • Fixed shape and volume.

    • Strong forces of attraction between particles.

    • Particles have a fixed pattern (lattice).

    • Atoms vibrate but cannot change position.

  • Liquid

    • Fixed volume but changes shape depending on the container.

    • Weaker attractive forces than solids.

    • No fixed pattern.

    • Particles slide past each other.

  • Gas

    • No fixed shape or volume; gases fill up their containers.

    • Almost no intermolecular forces.

    • Particles are far apart and move quickly.

    • Gases spread out to fill the container and exert equal pressure on all surfaces.

    • Particles collide with each other and bounce in all directions.

Internal Energy of Matter

  • The total energy stored by the particles making up a substance or system.

    • Depends on the space between molecules (potential energy, E_p).

    • Depends on its temperature (kinetic energy, E_k).

  • Potential Energy: E_p of gas > liquid > solid

  • Kinetic Energy: E_k of gas > liquid > solid

Changes in State of Matter

  • Melting (solid > liquid)

    • Solid at melting point absorbs thermal energy to break intermolecular forces and separate molecules, so potential energy increases.

    • Temperature is constant at melting point; kinetic energy of molecules is constant.

    • Internal energy increases when solid changes into liquid.

  • Freezing (liquid > solid)

    • Liquid at melting point removes thermal energy to create intermolecular forces and reduce separation between molecules, so potential energy decreases.

    • Temperature is constant at freezing; kinetic energy of molecules is constant.

    • Internal energy decreases when liquid is changed into solid.

  • Boiling (liquid > gas)

    • Liquid at boiling point absorbs thermal energy to break intermolecular forces and separate molecules, so potential energy increases.

    • Temperature is constant at boiling point; kinetic energy of molecules is constant.

    • Internal energy increases when liquid is changed into gas.

  • Condensation (gas > liquid)

    • Gas at boiling point removes thermal energy to create intermolecular forces and reduce the separation between molecules, so potential energy decreases.

    • Temperature is constant during condensation; kinetic energy of molecules is constant.

    • Internal energy decreases when gas changes into liquid.

2.1.2 Particle Model

Arrangement, Separation, and Motion in Different States:

  • Solid

    • Arrangement: Particles are tightly packed in a regular, fixed pattern.

    • Separation: Particles are very close together with little space between them.

    • Motion: Particles only vibrate in place; they do not move around.

  • Liquid

    • Arrangement: Particles are randomly arranged but still quite close to each other.

    • Separation: Particles are close together but have small gaps, allowing them to move.

    • Motion: Particles move and slide past each other slowly, which is why liquids can flow.

  • Gas

    • Arrangement: Particles are randomly arranged and spread far apart.

    • Separation: Particles are very far apart with large space between them.

    • Motion: Particles move quickly in all directions, colliding with each other and the walls of their container.

Motion and Temperature

  • As temperature increases, particles move faster.

  • Particles gain kinetic energy (energy of movement) when heated.

  • Lower temperature means slower-moving particles with less kinetic energy.

Pressure and Changes in Pressure of a Gas

  • Gas Pressure: Caused by collisions of gas particles with the walls of their container.

  • Changes in Pressure:

    • If temperature increases, gas particles move faster and collide more often and harder with the container walls, increasing pressure.

    • If the volume of the container decreases (with the same number of particles), the particles collide more often with the walls because they have less space to move, which also increases pressure.

    • More particles in the same space also means more collisions, leading to higher pressure.

Brownian Motion

  • Random movement of microscopic particles (like pollen) in a liquid or gas.

  • Microscopic particles are hit by the moving particles of the fluid around them (like water molecules or air particles).

  • The motion is random because the particles in the fluid collide from different directions with varying forces, making the microscopic particles move unpredictably.

2.1.3 Gases and the Absolute Scale of Temperature

Effect on the Pressure of a Fixed Mass of Gas:

  • Change of Temperature at Constant Volume:

    • When temperature increases, gas particles gain more kinetic energy and move faster.

    • This leads to more frequent and harder collisions with the walls of the container, which increases the pressure.

    • At constant volume, higher temperature always results in higher pressure because the particles are confined to the same space and collide more often with more force.

  • Change of Volume at Constant Temperature:

    • When volume increases (container expands), gas particles have more space to move, so they collide with the wall less often, resulting in lower pressure.

    • When volume decreases (container contracts), particles collide with the walls more frequently, leading to higher pressure.

    • If temperature remains constant, increasing the volume will reduce the pressure, and decreasing the volume will increase the pressure.

Relationship Between Pressure and Volume

  • \frac{p1V1}{T1} = \frac{p2V2}{T2}

  • p_1 = initial pressure exerted by the gas

  • V_1 = initial volume occupied by the gas

  • p_2 = final pressure exerted by the gas

  • V_2 = final volume occupied by the gas

Converting Temperatures Between Kelvin and Celsius

  • Kelvin (K) is the absolute temperature scale, starting from absolute zero (-273℃).

  • The relation between Kelvin and Celsius is: T(K) = θ(℃) + 273

    • To convert from Celsius to Kelvin: Add 273 to the Celsius temperature. Example: 25℃ + 273 = 298K

    • To convert from Kelvin to Celsius: Subtract 273 from the Kelvin temperature. Example: 300K - 273 = 27℃

Relationship Between Pressure and Volume of a Gas (Boyle’s Law)

  • Boyle’s Law states that for a fixed mass of gas at constant temperature, the pressure p and the volume V are inversely proportional.

  • This means when the volume increases, pressure decreases and vice versa, provided temperature remains constant.

  • The relationship is expressed mathematically as: pV = constant