Module 5 : Newtonian World and Astrophysics
Module 5 – Newtonian World and Astrophysics
Thermal physics (5.1)
Temperature (5.1.1)
Thermal equilibrium (also referred to as t.e. in these notes)
• Net thermal energy transfer in system is equal to zero
• Objects in the system at that are at t.e. are at the same temperature
• Unless t.e., there will always be net energy transfer but the system will eventually reach t.e.
• Two objects touching with dashes along the touching edge signifies t.e. between them
• If two objects either side of another in t.e. then middle object also in t.e. with each object
• Energy always transfers (through heat) from hotter object to colder object to maintain t.e.
Absolute scale and absolute zero
• Absolute scale: scale for measuring temp. based on absolute zero and triple point of water
• Absolute zero: lowest possible temp. at which substances have minimum internal energy
• Kelvin: SI base unit of absolute (thermodynamic) scale of temperature
• Absolute zero = –273°C or 0 K ∴ conversions: °C to K = +273 ∴ K to °C = –273°C
Solid, liquid and gas (5.1.2)
Kinetic models
• Solids
o Arrangement: regular
o Spacing: very close together, tightly packed
o Motion: vibrate about a fixed position
o Intermolecular forces: very strong
o Energy of atoms/molecules: low kinetic and heat energy
• Liquids
o Arrangement: irregular, quite random but structure varies from moment to moment
o Spacing: close together, but less than solids; more tightly packed than gas molecules
o Motion: move over/on top of each other, liquids ‘flow’
o Intermolecular forces: not strong, moderate; weaker than solids, stronger than gas
o Energy of atoms/molecules: higher than that of solids, lower than that of gases
• Gases
o Arrangement: totally random, no arrangement at all with a chaotic pattern
o Spacing: very far apart
o Motion: fast and random
o Intermolecular forces: very weak, almost negligible as particles are so far apart
o Energy of atoms/molecules: very high kinetic and heat
Brownian motion
• Continuous fast, random motion of gas molecules / small particles, suspended in fluid
• Whitley Bay Smoke Cell experiment:
o Wires connected to power supply DC on one end and attached to ends of smoke cell
o Smoke cell placed underneath microscope with small glass tube inside it
o Paper straw set alight on one end and held at a steep angle so the flame is upwards
o Smoke exits from bottom of straw which is held above tube to be collected in there
o Once glass tube full, cover slip placed quickly on top of tube so smoke can’t escape
o Down microscope you can see little dots moving slowly, showing Brownian motion
o Gas molecules very small compared to large smoke particulates
o Gas molecules must be moving very fast as their mass is small and particulates must
be moving slowly due to their relatively larger mass as momentum is conserved
1|Page Rhea Modi
, Module 5 : Newtonian World and Astrophysics
Internal energy
• Internal energy: sum of the random distribution of kinetic and potential energies associated
with the atoms, ions, or molecules of a system / within a substance
• Kinetic energy: motion/movement of particles
• Potential energy: spacing of particles: more attraction = less “potential” to move about
• Absolute zero = lowest limit for temperature ∴ here, substance has minimum internal energy
• Factors changing the kinetic and potential energies of a system hence its internal energy:
o Temperature
o Pressure
o Volume
o Amount of substance (moles): measure of amount of matter in moles
• Change in temperature in a system
o Heat energy converted into kinetic energy
o Particles vibrate/move more when temperature increased
o Kinetic energy increased ∴ internal energy increased
• Change in state in a system
o Heat energy converted into potential energy
o When state changes from solid-liquid / liquid-gas, spacing between atoms increased
o Potential energy increased ∴ internal energy increased
• NB: state/phase change = temperature constant as heat energy used up in state change
Thermal properties of materials (5.1.3)
Specific heat capacity
• The energy required per unit mass to change temperature by 1K or 1°C
• 𝑬 = 𝒎𝒄∆𝜽 where ∆𝜽 = temperature change (in °C or K as intervals are same on both)
Electrical experiment for specific heat capacity
• 𝑸 = 𝒎𝒄∆𝑻 where Q = heat energy transferred, and T = temperature
𝑸
• 𝒄 = 𝒎∆𝑻
• 𝑾 = 𝑷𝒕 = 𝑽𝑰𝒕 = 𝑸
𝑽𝑰𝒕
• 𝒄=
𝒎∆𝑻
• Set up experiment with power supply connected to ammeter and metal block in series with
a voltmeter connected to the metal block in parallel
• Measure initial and final temperature with thermometer, and I and V readings (which will
only slightly fluctuate throughout experiment) whilst using stopwatch to calculate c
Specific latent heat of fusion and vaporisation
• SLH of fusion: energy needed to change the phase of a unit mass of a substance at melting
point from solid to liquid without changing temperature
• SHL of vaporisation: energy needed to change the phase of a unit mass of a substance at
boiling point from liquid to gas without changing temperature
• 𝑬𝒉 = 𝒎𝑳 where Eh = heat energy (J), m = mass of liquid/gas changing state, L = specific
latent heat of fusion/vaporisation (J kg-1)
Electrical experiment to determine SLH of fusion
• Energy transferred to a substance increases its internal energy without increasing its
temperature
• A heating circuit can be used, like the one used to determine specific heat capacity
• Thermometer should be used to ensure ice is at melting point and not a lower temperature
• Ice should be seen just starting to melt before heater is switched on
• Measure p.d. across heater, current in heater, and time during which heater is used
𝑬 𝑰𝑽𝒕
• Use this to work out energy transferred to ice: 𝑬 = 𝑰𝑽𝒕 so 𝑳𝒇 = 𝒎𝒉 = 𝒎
• Important to accurately measure mass of substance that changes phase (ice in this case)
2|Page Rhea Modi
, Module 5 : Newtonian World and Astrophysics
Electrical experiment to determine SLH of vaporisation
• Energy required to change substance from liquid phase to gaseous phase at boiling point
often considerably more than its SLH of fusion, due to much larger difference between
internal energy of gas and liquid than between liquid and solid
o ∴ Lv > Lf for most substances
• An electrical heater is used with a condenser to collect the vapour
• Then measure the mass of the liquid that is changing phase
• Same equation as above used for working out SLH of fusion, but this experiment works out
SLH of vaporisation with mass = mass of liquid that is changing phase, whereas above uses
mass = mass of solid changing phase
Ideal gases (5.1.4)
Model of kinetic theory of gases
• Ideal gas: model of a gas including assumptions that simplify the behaviour of real gases
• Kinetic model: model that describes all substance as made of atoms, ions, or molecules,
arranged differently depending on phase of substance
• Amount of substance in moles: Avogadro constant NA = 6.02 × 1023 mol–1
• 𝑵 = 𝒏 × 𝑵𝑨 where N = number of molecules, n = number of moles, NA = Avogadro constant
• Assumptions for this model:
o Large number of molecules in random, rapid motion (Brownian motion)
o Particles (atoms/molecules) occupy negligible volume compared to volume of gas
o Collisions perfectly elastic and time = negligible compared to time between collisions
o Negligible forces between particles except during collision
• Using assumptions and Newton’s laws, we explain how particles in ideal gas cause pressure:
o When gas particles collide with container wall, velocity is +u before collision and –u
after collision, so momentum is +mu before and –mu after
o Therefore, total change in momentum = –2mu
∆𝒑 −𝟐𝒎𝒖
o N2L: ∆𝒕 = ∆𝐭 where Δt = time between collisions with wall
o 3rd law: particle also exerts equal but opposite force on wall
o Large number of particles collide with wall
−𝟐𝒎𝒖
o If total force of all these particles is F, then pressure is F/A = 𝑨∆𝒕
−𝟐𝒎𝒖
o Relating 𝒑 = 𝑨∆𝒕 and 𝒑𝑽 = 𝒏𝑹𝑻:
▪ Increase in T leads to increase in u leads to increase in p
▪ Increase in V leads to increase in A leads to decrease in p
Molar mass (beyond the specification, but useful to know anyway)
• Mass of one mole of a substance
• Units: kg mol-1
• 𝒎 = 𝒏 × 𝑴 where m = mass of substance, n = no. of moles, M = molar mass
Equation of a state of an ideal gas
• 𝒑𝑽 = 𝒏𝑹𝑻 : n = no. of moles (mol), R = 8.31 J mol–1 K–1, T = absolute (in Kelvin) temperature
• Unlike specific heat capacity, this is not a change in temperature so always convert to Kelvin
• As well as the constant quantities stated below, in each case, there is a fixed mass
Applications of this equation
• When temperature is constant: BOYLE’S LAW
o 𝒑𝑽 = 𝒏𝑹𝑻 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕
o => 𝒑𝑽 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕
𝟏
o => 𝒑 ∝ 𝑽
o Graph 1:
▪ Pressure by volume
▪ Negative exponential with both axes as asymptotes
3|Page Rhea Modi
Module 5 – Newtonian World and Astrophysics
Thermal physics (5.1)
Temperature (5.1.1)
Thermal equilibrium (also referred to as t.e. in these notes)
• Net thermal energy transfer in system is equal to zero
• Objects in the system at that are at t.e. are at the same temperature
• Unless t.e., there will always be net energy transfer but the system will eventually reach t.e.
• Two objects touching with dashes along the touching edge signifies t.e. between them
• If two objects either side of another in t.e. then middle object also in t.e. with each object
• Energy always transfers (through heat) from hotter object to colder object to maintain t.e.
Absolute scale and absolute zero
• Absolute scale: scale for measuring temp. based on absolute zero and triple point of water
• Absolute zero: lowest possible temp. at which substances have minimum internal energy
• Kelvin: SI base unit of absolute (thermodynamic) scale of temperature
• Absolute zero = –273°C or 0 K ∴ conversions: °C to K = +273 ∴ K to °C = –273°C
Solid, liquid and gas (5.1.2)
Kinetic models
• Solids
o Arrangement: regular
o Spacing: very close together, tightly packed
o Motion: vibrate about a fixed position
o Intermolecular forces: very strong
o Energy of atoms/molecules: low kinetic and heat energy
• Liquids
o Arrangement: irregular, quite random but structure varies from moment to moment
o Spacing: close together, but less than solids; more tightly packed than gas molecules
o Motion: move over/on top of each other, liquids ‘flow’
o Intermolecular forces: not strong, moderate; weaker than solids, stronger than gas
o Energy of atoms/molecules: higher than that of solids, lower than that of gases
• Gases
o Arrangement: totally random, no arrangement at all with a chaotic pattern
o Spacing: very far apart
o Motion: fast and random
o Intermolecular forces: very weak, almost negligible as particles are so far apart
o Energy of atoms/molecules: very high kinetic and heat
Brownian motion
• Continuous fast, random motion of gas molecules / small particles, suspended in fluid
• Whitley Bay Smoke Cell experiment:
o Wires connected to power supply DC on one end and attached to ends of smoke cell
o Smoke cell placed underneath microscope with small glass tube inside it
o Paper straw set alight on one end and held at a steep angle so the flame is upwards
o Smoke exits from bottom of straw which is held above tube to be collected in there
o Once glass tube full, cover slip placed quickly on top of tube so smoke can’t escape
o Down microscope you can see little dots moving slowly, showing Brownian motion
o Gas molecules very small compared to large smoke particulates
o Gas molecules must be moving very fast as their mass is small and particulates must
be moving slowly due to their relatively larger mass as momentum is conserved
1|Page Rhea Modi
, Module 5 : Newtonian World and Astrophysics
Internal energy
• Internal energy: sum of the random distribution of kinetic and potential energies associated
with the atoms, ions, or molecules of a system / within a substance
• Kinetic energy: motion/movement of particles
• Potential energy: spacing of particles: more attraction = less “potential” to move about
• Absolute zero = lowest limit for temperature ∴ here, substance has minimum internal energy
• Factors changing the kinetic and potential energies of a system hence its internal energy:
o Temperature
o Pressure
o Volume
o Amount of substance (moles): measure of amount of matter in moles
• Change in temperature in a system
o Heat energy converted into kinetic energy
o Particles vibrate/move more when temperature increased
o Kinetic energy increased ∴ internal energy increased
• Change in state in a system
o Heat energy converted into potential energy
o When state changes from solid-liquid / liquid-gas, spacing between atoms increased
o Potential energy increased ∴ internal energy increased
• NB: state/phase change = temperature constant as heat energy used up in state change
Thermal properties of materials (5.1.3)
Specific heat capacity
• The energy required per unit mass to change temperature by 1K or 1°C
• 𝑬 = 𝒎𝒄∆𝜽 where ∆𝜽 = temperature change (in °C or K as intervals are same on both)
Electrical experiment for specific heat capacity
• 𝑸 = 𝒎𝒄∆𝑻 where Q = heat energy transferred, and T = temperature
𝑸
• 𝒄 = 𝒎∆𝑻
• 𝑾 = 𝑷𝒕 = 𝑽𝑰𝒕 = 𝑸
𝑽𝑰𝒕
• 𝒄=
𝒎∆𝑻
• Set up experiment with power supply connected to ammeter and metal block in series with
a voltmeter connected to the metal block in parallel
• Measure initial and final temperature with thermometer, and I and V readings (which will
only slightly fluctuate throughout experiment) whilst using stopwatch to calculate c
Specific latent heat of fusion and vaporisation
• SLH of fusion: energy needed to change the phase of a unit mass of a substance at melting
point from solid to liquid without changing temperature
• SHL of vaporisation: energy needed to change the phase of a unit mass of a substance at
boiling point from liquid to gas without changing temperature
• 𝑬𝒉 = 𝒎𝑳 where Eh = heat energy (J), m = mass of liquid/gas changing state, L = specific
latent heat of fusion/vaporisation (J kg-1)
Electrical experiment to determine SLH of fusion
• Energy transferred to a substance increases its internal energy without increasing its
temperature
• A heating circuit can be used, like the one used to determine specific heat capacity
• Thermometer should be used to ensure ice is at melting point and not a lower temperature
• Ice should be seen just starting to melt before heater is switched on
• Measure p.d. across heater, current in heater, and time during which heater is used
𝑬 𝑰𝑽𝒕
• Use this to work out energy transferred to ice: 𝑬 = 𝑰𝑽𝒕 so 𝑳𝒇 = 𝒎𝒉 = 𝒎
• Important to accurately measure mass of substance that changes phase (ice in this case)
2|Page Rhea Modi
, Module 5 : Newtonian World and Astrophysics
Electrical experiment to determine SLH of vaporisation
• Energy required to change substance from liquid phase to gaseous phase at boiling point
often considerably more than its SLH of fusion, due to much larger difference between
internal energy of gas and liquid than between liquid and solid
o ∴ Lv > Lf for most substances
• An electrical heater is used with a condenser to collect the vapour
• Then measure the mass of the liquid that is changing phase
• Same equation as above used for working out SLH of fusion, but this experiment works out
SLH of vaporisation with mass = mass of liquid that is changing phase, whereas above uses
mass = mass of solid changing phase
Ideal gases (5.1.4)
Model of kinetic theory of gases
• Ideal gas: model of a gas including assumptions that simplify the behaviour of real gases
• Kinetic model: model that describes all substance as made of atoms, ions, or molecules,
arranged differently depending on phase of substance
• Amount of substance in moles: Avogadro constant NA = 6.02 × 1023 mol–1
• 𝑵 = 𝒏 × 𝑵𝑨 where N = number of molecules, n = number of moles, NA = Avogadro constant
• Assumptions for this model:
o Large number of molecules in random, rapid motion (Brownian motion)
o Particles (atoms/molecules) occupy negligible volume compared to volume of gas
o Collisions perfectly elastic and time = negligible compared to time between collisions
o Negligible forces between particles except during collision
• Using assumptions and Newton’s laws, we explain how particles in ideal gas cause pressure:
o When gas particles collide with container wall, velocity is +u before collision and –u
after collision, so momentum is +mu before and –mu after
o Therefore, total change in momentum = –2mu
∆𝒑 −𝟐𝒎𝒖
o N2L: ∆𝒕 = ∆𝐭 where Δt = time between collisions with wall
o 3rd law: particle also exerts equal but opposite force on wall
o Large number of particles collide with wall
−𝟐𝒎𝒖
o If total force of all these particles is F, then pressure is F/A = 𝑨∆𝒕
−𝟐𝒎𝒖
o Relating 𝒑 = 𝑨∆𝒕 and 𝒑𝑽 = 𝒏𝑹𝑻:
▪ Increase in T leads to increase in u leads to increase in p
▪ Increase in V leads to increase in A leads to decrease in p
Molar mass (beyond the specification, but useful to know anyway)
• Mass of one mole of a substance
• Units: kg mol-1
• 𝒎 = 𝒏 × 𝑴 where m = mass of substance, n = no. of moles, M = molar mass
Equation of a state of an ideal gas
• 𝒑𝑽 = 𝒏𝑹𝑻 : n = no. of moles (mol), R = 8.31 J mol–1 K–1, T = absolute (in Kelvin) temperature
• Unlike specific heat capacity, this is not a change in temperature so always convert to Kelvin
• As well as the constant quantities stated below, in each case, there is a fixed mass
Applications of this equation
• When temperature is constant: BOYLE’S LAW
o 𝒑𝑽 = 𝒏𝑹𝑻 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕
o => 𝒑𝑽 = 𝒄𝒐𝒏𝒔𝒕𝒂𝒏𝒕
𝟏
o => 𝒑 ∝ 𝑽
o Graph 1:
▪ Pressure by volume
▪ Negative exponential with both axes as asymptotes
3|Page Rhea Modi
