phys cba1 notes!

kinetic particle model of matter

matter

• matter is made up of tiny particles in continuous, random motion

  • note: singular air particles move in one direction. if asked to draw the motion of ONE air particle, it can be drawn bouncing off surfaces. however, when asked to draw the motion of an air particle among a large number of air molecules, it would have to hit other air particles on the way → the path will appear to be zigzagged.

brownian motion

• refers to the random motion of tiny particles suspended in a fluid (e.g. smoke in air or pollen in water)

  • in experiment, bright specks of light (which are the smoke particles) were observed to be moving about in a constant, random motion.

  • this is because the smaller air particles are also in constant, random motion. the air particles collide unevenly with the larger smoke particles (from all directions) and exert a resultant force on the smoke particles. the smoke particles move in the direction of the resultant force, as in Newton’s 2nd Law of Motion.

  • only particles that are relatively big enough to be seen, and that are light enough to be moved by air particles can be used in above experiment.

kinetic model of matter

property	solid	liquid	gas
diagram representation of particles
arrangement	orderly arrangement, packed closely together	not in orderly arrangement. packed closely together	not in orderly arrangement, far apart from each other
motion	vibrate about a fixed position (low KE)	free to move around within vessel and slide over each other	free to move at high speeds (high KE)
force of attraction	very strong attractive forces	strong attractive forces	weak attractive forces

properties in relation to states

• its generally true that the volume of substance in the solid state is equal to the volume of substance in the liquid state.

temperature of matter and kinetic energy

• as the temperature of energy increases, the kinetic energy it possesses will increase as well.

  • note: during change of state, energy is related to potential energy, average kinetic energy stays the same during state change. hence:

    • when a piece of ice melts, intermolecular forces between molecules become weaker while the molecules move faster.

    • when a substance is heated without any change in state, the intermolecular forces stay the same while the molecules move faster. (distance stays the same)

    • when spacing between particles increases, its potential energy increases.

gases

equations: (relationship: one causes the other)

• P₁/T₁  =  P₂/T₂

• V₁/T₁ = V₂/T₂ 

• P₁V₁  = P₂V₂ 

• P₁V₁ / T₁  = P₂V₂ / T₂ 

PV = nRT: this equation is not tested, but can be used to remember the relationships between different variables. main variables to be tested are pressure, temp and volume only.

• P → pressure

• V → volume

• n → no. of moles

• R → universal gas constant

• T → temperature (Kelvin)

pressure vs temperature	volume vs temperature	pressure vs volume
as temp increases, the average KE of gas molecules increases, and the molecules move faster and collide with the walls of the container more frequently and with greater force.  since pressure = force per unit area, the gas pressure increases.	as temp increases, the average KE of gas molecules increases, and the molecules move faster and collide with the walls of the container more frequently and with greater force.  if pressure is kept constant, the volume of the gas needs to increase.	as volume increases, the number of gas molecules per unit volume decreases. there are less frequent collisions with the wall of the container, resulting in a lower force per unit area being exerted. hence, pressure decreases.

faqs and notes

notes:

• volume is directly related to distance between particles. (as volume increases, distance between particles also increases ALWAYS → given the no. of particles remains the same)

• frequency of collisions and speed of particles are both INDIVIDUALLY directly related to pressure:

  • if pressure remains unchanged at a higher temp, we would expect some other variable (volume and temp) to have changed such that the frequency of collisions decreases.

  • cannot say gas molecules gained TE: TE is supplied to the gas and is converted to KE of the molecules.

thermal properties of matter

temperature

• measures the concentration of thermal energy

  • temperature is a property of a material, and hence depends on the material, whereas TE is a form of energy existing on its own.

celsius and kelvin scale

• T_k = T_c + 273.15

• at zero kelvin, molecules have stopped moving and the pressure would be 0.

heat

• a measure of how much thermal energy is transferred from one body to another. transfer of energy from one body to another is a result of temperature differences between them.

thermal equilibrium

• net heat flows from hotter to colder object, until both are of the same temperature. both objects are said to be in thermal equilibrium when there is no net heat flow between them. (there is still heat flow, just no NET heat flow.

  • zeroth law of thermal dynamics (NOT TESTED): when a body A is in thermal equilibrium with another body B, and also separately in thermal equilibrium with a body C, then both body B and C will also be in thermal equilibrium with each other.

internal energy

• internal energy of a body is the total kinetic energy due to the motion of the molecules and potential energy due to the intermolecular forces in the body (IE = KE + PE)

heat capacity

• heat capacity of a body is the quantity of thermal energy needed to cause its temperature to change by 1ºC or 1K.

  • unit: J ^oC^-1   or   J K^-1 (if value given by the question has this unit, do not use mass in calculations)

  • heat capacity depends on substances the object is made up of and mass of substances in the body.

  • formula: Q = c Δθ

    • c → heat capacity (J ^oC^-1   or   J K^-1)

• specific heat capacity: the quantity of thermal energy needed to change the temperature of 1kg of substance by 1ºC or 1K. (divided by the mass)

  • formula: Q = mc Δθ

    • Q → thermal capacity/energy of object (J)

    • c → specific heat capacity (J kg^{-1 o}C^-1   or   J kg^-1 K^-1)

    • Δθ → change in temperature (ºC or K)

    • m → mass

phase change (change of state)

• no net change of temperature during phase change → this is a concept called latent heat

  • latent heat (L) → amount of thermal energy absorbed/released during a change of state without a change in temperature (J)

  • specific latent heat → energy needed to change the state of m kg of a substance without a change in temperature (J kg^-1)

    • formula:  L = ml_f   or   ml_v   (write Q = ml)

      • L → latent heat

      • m → mass

      • l_f → specific latent heat of fusion

      • l_v → specific latent heat of fusion

Heating Curve - Melting

from P to Q, the average K.E of the molecules increases. from Q to R, thermal energy is absorbed to weaken the bonds of the solid particles and potential Energy increases.  kinetic energy remains the same as the temperature is constant latent heat of fusion: the amount of thermal energy required to change a substance from a solid to a liquid (or vice versa) without a change in temperature.

Heating Curve - Boiling

from X to Y, the average K.E of the molecules increases. from Y to Z, P.E increased.  energy absorbed to break the intermolecular bonds of water molecules and potential energy increases.  kinetic energy remains the same as the temperature is constant latent heat of vaporisation: The amount of thermal energy required to change a substance from a liquid to gas (or vice versa) without a change in temperature.

• sublimation → solid to gas

• deposition → gas to solid

boiling vs. evaporation

evaporation

• causes cooling: molecules that are evaporated gain TE from surroundings, and escape as vapour, carrying thermal energy away from the liquid

• factors affecting rate of evaporation:

  • temperature: higher temperature, higher rate of evaporation

  • surface area: greater surface area, higher rate of evaporation

  • humidity: higher humidity, lower rate of evaporation

  • pressure: higher pressure, lower rate of evaporation

cooling curve

heating curve

faqs and notes

notes:

• look out for “specific heat capacity” and “heat capacity”. when explaining why an object is better for a certain purpose, use “specific heat capacity” → you are comparing the material itself directly

• “per degree celsius” and “per kelvin” are the same

• working:

general notes:

•  the length of any arrows should be drawn representative of the relative magnitude of the forces it represents 

• can use the answer that has been rounded off in part (a) to solve part (b)

• when asked to state a quantity that needs to be measured in order to determine something, state it specifically, as if in a lab practical (e.g mass OF the block)

• standard form: not required unless asked, no rule of thumb