density

Density

  • Definition: Mass per unit volume

    • Formula: \rho = \frac{m}{V}

    • Units: Typically expressed in kgm$^{-3}$

  • Factors Affecting Density:

    • Depends on the spacing of atoms in matter.

    • Solids and liquids have similar densities due to minimal change in particle spacing.

    • Generally, liquids have lower density than solids (with the notable exception of ice being less dense than water).

    • Gases have significantly lower densities because molecule spacing increases by about ten times due to higher energy levels which causes greater volume increases.

  • Important Note: During a change of state, mass remains constant.

    • If 20g of liquid evaporates, the gas produced weighs 20g as well.

Changes of State

  • Mass Conservation: Mass is conserved during phase changes.

  • Reversibility: Physical changes are reversible, contrasting with chemical changes where original properties are not retained.

    • Examples of changes of state:

    • Melting

    • Freezing

    • Evaporating

    • Condensing

    • Sublimation (solid to gas)

Heating a System

  • Effect on Particles: Heating increases energy in particles.

    • Increased particle vibration leads to higher system temperature or a change in state.

    • The “system” can refer to any state of matter, such as an ice cube or a gas.

Specific Heat Capacity

  • Definition: The energy required to raise the temperature of 1 kg of a substance by 1°C (which is equivalent to 1 K).

    • Formula: E = mc\Delta T

    • Units: Jkg$^{-1}$°C$^{-1}$

Specific Latent Heat

  • Definition: Energy necessary to change the state of 1 kg of a substance without changing its temperature.

    • Must be at the proper temperature for the change to occur.

    • Types:

    • Specific Latent Heat of Fusion: Energy required for melting/freezing.

    • Specific Latent Heat of Vaporisation: Energy needed for boiling/condensation.

    • Energy absorbed during melting and evaporating; released when freezing and condensing.

    • Formula: E = ml

    • Units: Jkg$^{-1}$

Insulation

  • Concept: Thermal energy escapes systems, leading to energy wastage.

    • Use of thermal insulators, such as foam, helps reduce energy loss (as they are poor thermal conductors).

    • Reflective coatings can be used to send Infrared (IR) radiation back into the system.

    • Considerations in insulation: Analyze the situation to optimize energy retention.

Pressure of a Gas

  • Gas Behavior: Gas particles move randomly in all directions.

    • A “fluid” encompasses both liquids and gases.

    • Formula for pressure: \text{Pressure} = \frac{\text{Force}}{\text{Area}}

  • Pressure Dynamics:

    • Pressure produces a net force perpendicular to any surface.

    • Collisions with surfaces cause changes in particle velocity and momentum, translating into force exerted on the wall.

    • Relationship between temperature and pressure at constant volume:

    • Increased temperature leads to accelerated particles that collide more frequently and with greater force, increasing pressure.

Absolute Zero

  • Definition: The lowest possible temperature at 0 K or -273°C.

    • At this temperature, particles possess no energy and do not vibrate, remaining completely still.

  • Conversion: To convert Kelvin to Celsius:

    • Formula: T_{\text{kelvin}} = T - 273

    • Example: 4K = -269°C and 0°C = 273K

Pressure Changes (Physics Only)

  • Behavior Under Pressure: Gases naturally strive to maintain a consistent temperature.

    • Increasing pressure results in gas compression (decreasing volume).

    • Higher pressure implies greater force over a smaller area.

    • Reduced volume leads to a higher incidence of particle collisions, which maintains velocity (affecting pressure).

    • The relationship indicates: Pressure is inversely proportional to volume.

    • Formula: For a gas at fixed mass and temperature: P1V1 = P2V2, where P is pressure and V is volume at states 1 and 2.

Doing Work on a Gas (Physics Only)

  • Temperature Increase: Work done on a gas leads to increased temperature.

    • Work done formula: W = \text{Force} \times \text{Distance} = \text{Pressure} \times \text{Volume}

Adding More Particles to a Fixed Volume (Physics Only)

  • Effect of Compression:

    • Compressing/expanding a gas changes its volume.

    • Introducing more gas into a fixed volume increases particle number, leading to more frequent collisions with the walls, thus increasing pressure.

    • Energy transfer occurs as more gas elevates temperatures.

Fixed Number of Particles with Decreasing Volume (Physics Only)

  • Collision Dynamics:

    • Particles collide with inwardly moving walls, gaining momentum (higher rebound velocity than approach velocity).

    • Increased velocity causes a rise in pressure due to more frequent collisions.

    • Temperature increases as the kinetic energy of particles rises during compression.