thermal physics

define internal energy

• sum of the randomly distributed kinetic energies and potential energies of the particles / molecules in a sample / substance

internal energy of a system is increased when

energy is transferred to it

• by heating or

• when (mechanical) work is done on it

during a state change

• total potential energies of particles changing

• total kinetic energies constant - temp constant

specific heat capacity

• Q=mc∆θ

• the energy required to raise the temperature 1kg of a substance by 1K

specific latent heat

• Q = ml

when temperatures is changing

• total kinetic energy is changing

• total potential energy is constant

how atoms change their arrangement during melting or boiling

• energy transferred into system reduces the number of nearest atomic partners / atoms move their centre of vibration

• break some atomic bonds

how motion of the atoms changes during temperature rise

• temperature is a measure of the mean kinetic energy of particles in a substance )and determines the direction of heat flow)

• mean kinetic energy of the atoms increases so their mean speed increases

heat

the transfer of thermal energy from regions of lower temperature to regions of higher temperature

specific latent heat of fusion

• energy required to change a unit mass (1kg) of a substance from the solid state to the liquid state

• without temperature change

• (when it is at melting temperature - must gain enough energy to reach its melting temperature first)

temperature increase of air when speed of pump is higher

• greater work done on air molecules

• increases mean speed of articles and mean square speed

• therefore increases kinetic energy and temperature by 1st law of thermodynamics

pressure

• force per unit area that it exerts normally to the surfaces of a container

• due to collisions with container walls

• each atom exerts a force on container wall due to experiencing a change in momentum over a time

• larger force caused by more collisions per second and more forceful collisions (greater total momentum change per second) per unit area

• container wall exerts equal and opposite force on each particle

pressure and temperature

• increasing temperature increases mean ke and mean speed of gas particles

• greater rate of change in momentum during each collision with walls

• time between successive collisions also decreases so more collisions per second

• larger force over same area per second

volume and temperature

• increasing temperature increases the mean speed of gas particles

• faster molecules would result in greater change in momentum per collision - increasing pressure

• volume (of non fixed container) would increase to reduce collisions per second by increasing distance travelled between successive collisions, maintaining constant pressure

boyle’s law

• pressure is inversely proportional to the volume at a constant temperature for a fixed mass of gas

• $$P1V1=P2V2$$

• isothermal - any change at a constant temperature

charles’s law

• volume is proportional to its temperature at a constant pressure for a fixed mass of gas

• $$\frac{V1}{T1}=\frac{V2}{T2}$$

• isobaric - any change at a constant pressure

pressure law

• the pressure is directly proportional to its temperature at a constant volume for a fixed mass of gas

• $$\frac{P1}{T1}=\frac{P2}{T2}$$

• isochoric - any change at a constant volume

ideal gas law

$$\frac{pV}{T}=cons\tan t$$

explaining gas laws

• assuming that a gas consists of point molecules

• moving at random

• continually colliding with container walls

• each impact causes causes a force on the container

• the force of many impacts is the cause of pressure of gas on container walls

• boyle’s law: reducing volume - gas molecules travel less distance between impacts - more impacts per second - greater pressure

• pressure law: raising temperature - average speed of the molecules increased - impacts with container walls are harder and more frequent - greater pressure

absolute 0

• temperature at which kinetic energy of the particles is 0 / random motion of particles stops

• 0k which is -273.15 Celsius

• a state of minimum internal energy

• using gas laws, plotting V or P against T, it is the temperature at which volume or pressure of a gas extrapolates to 0

degrees to kelvin

• +273

thermal equilibrium

• no overall heat transfer occurs between two objects at the same temperature

mean ke of gases with different molecular masses at same temperature / mixture at equilibrium

• same mean kinetic energy

work done on a gas at a constant pressure

$$W=P\Delta V$$

graph of pressure against volume

• area under graph is work done

number of moles, n in a mass

n = mass / molar mass

(molar mass is the mass of one mole)

number of molecules N

N = n x avogadro constant

ideal gas equation for number of moles

PV = nRT

• R is gas constant 8.31 Jmol^-1K^-1

• T is temperature in kelvin

• n is number of moles

ideal gas equation of number of molecules

PV = NkT

• k is boltzmann constant

• T is temperature in kelvin

• N is number of molecules

how boltzmann constant is related to gas constant

$$R=N_{A}k$$

brownian motion

• smoke particles moving in random motion

• movement of smoke particles caused by collisions with randomly moving air molecules

• smoke particles are visible but air particles are not hence air molecules must be very small

• smoke particles are continuously moving because the air molecules are continuously moving

• this is evidence for existence of atoms

molecular speeds in ideal gas

• continuous spread of speeds

• speed of individual molecule changes with collision with another molecule

• distribution same under constant temperature

• when gas temperature raised - molecules move faster on average - rms speed of molecules increases - distribution curve broader and flatter as more of the molecules moving at higher speeds

why gas particles must be in a vacuum to find their speed distribution at constant temperature

• so that gas atoms don’t lose ke and so speed due to collisions with air molecules

• as this would change the distribution of speeds

root mean square speed

• square speeds of individual molecules

• sum the squares and divide by number of molecules

• square root

kinetic theory model

$$pV=\frac13Nm\left(C_{rms}\right)^2$$

kinetic theory assumptions / definition of ideal gases

• point molecules of negligible volume compared to volume of gas

• do not attract each other - potential energies between particles assumed to be 0 - molecules move in straight lines between collisions ( as real gas molecules pull closer together, their potential energy drops below zero)

• continual random motion

• elastic collisions - no ke lost in collisions

• each collision with container surface is of much shorter duration than the time between impacts

internal energy for an ideal gas

• kinetic energy of the atoms

kinetic energy of one gas molecule

$$\frac12m\left(C_{rms}\right)^2=\frac32kT=\frac32\frac{RT}{2N_{A}}$$

gas laws vs kinetic theory

• gas laws are empirical (experimental) in nature

• kinetic theory model arises from theory

for ke of 1 mole

$\frac32kTN_{A}$ = $\frac32RT$

for ke of n moles (N particles)

$$\frac32nRT$$