unit 3: thermal physics

contained within a system or body (does NOT include environment, speed etc.), the sum of the random distribution of kinetic and potential energies of the objects atoms and molecules

the transfer of thermal energy from one body to another as a result of a difference in temperature, changes the internal energy of a system, symbol for heat is Q, unit is Joules

SI unit for temperature, ºC+273, objects cannot be at 0K because it means their particles are not moving

energy required to raise the temperature of a unit mass by one K/ºC without a change of state, measured in Jkg^-1K^-1

• Q=heat energy required in J

• m=mass in kg

• c=specific heat capacity in J Kg^-1K^-1

• ΔT=change in temperature in K

the total random kinetic energy of the particles of an object

no transfer of thermal energy occurs thus objects are at the same temperature

the specific heat equation

during changes of state heat is transferred but there is no change in temperature so Q=mcΔT doesn’t work

the heat transferred when there is a change of state

heat is taken from the environment

heat is released to the environment

melting and freezing

boiling and condensation

a phase change is a flat line on the graph of time against temperature

• more energy is required to boil water than melt ice, this is shown as the melting line is shorter than the boiling line on the graph

• therefore Lv > Lf for water

L is measured in Jkg-1 so must be multiplied by the amount of kilos for the total latent heat needed

when no heat is lost to the environment what is lost from one object is taken by the other object so |Q| will be the same but with opposite signs, what differs is the mass since Q is per kilogram

P1V1=P2V2

• for gas at a constant temperature, pressure is inversely proportional to volume

• the product of pressure and volume is a constant so if one changes the other one must too (unless the temperature changes)

• if pressure is doubled volume halves, what you multiply one by you must divide the other one by

m^3, 1 litre = a cube with each side measuring 10cm =10^-3 m^3 so 1000 litres = 1m^3

atm = atmospheres, 1atm =10^5 Pa, Pa=Nm^-2

V1/T1=V2/T2

• temperature must be Kelvins for this!

• volume and temperature are proportional — if one goes up so does the other

• what one is multiplied by the other must also be multiplied by

Gay-Lussac’s law: P1/T1=P2/T2

• temperature must be Kelvins for this!

• pressure and temperature are proportional — if one goes up so does the other

• what one is multiplied by the other must also be multiplied by

• (PV)(V/T)(P/T)= a constant

• by simplifying and taking the square root: PV/T = a constant (for a constant mass)

• V1/n1=V2/n2 (n = number of moles)

• for two separate gases at the same temperature and pressure, equal volumes of gases contain the same number of moles, thus volume is independent of the identity of the gas

• ratio of the volume to number of moles of two gases at the same temperature is always Avogadro’s constant

• constant is 6.02x10^23, called N_a

a quantity of a substance that contains a number of particles equal to the Avogadro constant and whose mass in grams is equal to the molar mass of the substance

• it is the quantity of a substance measured in moles

• number of molecules = number of moles x Avogadro’s constant, N=n x N_a

• the molar mass of the substance = mass of one mole of the substance

• substance of a mass = M_s/M (substance mass/molar mass)

• moles are ratios not physical units

a gas which obeys the ideal gas law for all values P, V and T

• Boyle’s law: P1V1=P2V2

• Charles’ law: V1/T1=V2/T2

• Gay-Lussac’s law: P1/T1=P2/T2

that only momentum changes when particles collide (hence ideal), all energy is conserved in the collision

• PV/T = constant which is nR — the number of moles multiplied by the molar gas constant which is 8.31 J K^-1 mol^-1

• therefore the ideal gas equation is PV=nRT with the temperature always in Kelvins

• or written as PV=NkT (not in data booklet) which works as k=R/Na and k is Boltzmann’s constant (1.38x10^-23 J K^-1)

• kinetic energy is proportional to temperature

• temperature is the average motion of things so doesn’t make sense for small numbers of particles but does for large numbers

• this is a macroscopic result, only valid for a lot of particles

thermal energy = average random kinetic energies of the particles in a substance = 3/2 N k_B T

• ideal gases have no potential energy whereas gases in reality have complex potential energy

• for ideal gases total energy = internal energy (U)

• U = 3/2 PV

  • U = total internal energy, as for ideal gases total = internal

  • Ek equation multiplied by N to make it total not average