Thermodynamics

Name	Definition	Formulae
Specific heat capacity	The amount of heat energy required to change the temperature of a unit mass of a substance by a unit temperature
Specific latent heat	The amount of heat energy required per unit mass of a substance to change the state from … to … at a constant temperature
KINETIC THEORY
Kinetic model of gas	Assumption: A gas is made of lots of particles Volume of particle << Volume of container Particles move at random Particles collide elastically (KE is conserved) No potential energy between particle (PE=0) The mean KE of particle is directly proportional to the temperature
Internal energy	Random distribution of potential and kinetic energy among the molecules
IDEAL GAS EQUATION
Ideal gas equation	$pV=frac{1}{3}Nm< c^{2}> =NKT=frac{1}{3}rho < c^{2}>$
Derive $pV=frac{1}{3}Nmc^{2}$	Initial x momentum: $mv_{x}$ Final x momentum: $-mv_{x}$ Time between collision: $t=frac{2L}{v_{x}}$ N2L, average force on wall $F=frac{Delta p}{t}=frac{2mv_{x}}{frac{2L}{v_{x}}}=frac{mv_{x}^{2}}{L}$ Total force on wall $sum_{all particles} frac{mv_{x}^{2}}{L}=frac{m}{L}sum v_{x}^{2}$ Mean squared speed $<c^{2}>=frac{sum (v_{x}^{2}+v_{y}^{2}+v_{z}^{2})}{N}$ Moving randomly: $sum v_{x}^{2}=sum v_{x}^{2}sum v_{y}^{2}=sum v_{x}^{2}$ $<c^{2}>=frac{3sum v_{x}^{2}}{N}$ $sum v_{x}^{2}=frac{N<c^{2}>}{3}$ Therefore, total force $F=frac{m}{L}times frac{N<c^{2}>}{3}$ $P=frac{F}{A}=frac{Nm<c^{2}>}{3L^{3}}$ But, $V=L^{3}$ so, $PV=frac{1}{2}Nm<c^{^{2}}>$
	Internal energy = KE + PE Fr ideal gas, PE = 0 so Internal energy = KE $U=sum frac{1}{2}m(v_{x}^{2}+v_{y}^{2}+v_{z}^{2})=frac{1}{2}Nm<c^{2}>$ $therefore PV=NKT=frac{2}{3}U$ $therefore U=frac{1}{2}Nmc^{2}=frac{2}{3}NKT$
Boyle’s Law	For a fixed amount of an ideal gas at a constant temperature: Its pressure is inversely proportional to its volume	$P_{1}V_{1}=P_{2}V_{2}$
Pressure Law	For a fixed amount of an ideal gas at a constant volume: Its pressure is directly proportional to its temperature	$frac{P_{1}}{T_{1}}=frac{P_{2}}{T_{2}}$
Charles’ Law	For a fixed amount of an ideal gas at a constant pressure: Its volume is directly proportional to its temperature	$frac{V_{1}}{T_{1}}=frac{V_{2}}{T_{2}}$
Absolute zero	The temperature at which the pressure/ volume of a gas become zero	$KE=frac{1}{2}m<c^{2}>=frac{3}{2}kT$
BLACK BODIES
Maxwell Boltzmann Distribution	How many molecules will have a speed in a small range of speed
Black bodies radiator	At every temperature above 0K objects radiate energy as electromagnetic wave A blackbody absorbs all the radiation that falls on it Total energy radiated per second only depends on the surface area A and the absolute temperature T
Stefan-Boltzmann Law	The total amount of energy radiated per second is proportional to the surface area A and the absolute temperature	$E=sigma AT^{4}$
Wein’s Law		$lambda _{max}T=2.898times 10^{3}=constant$