george notes Flashcards
Ideal gas equation
PV=1/3NM =2/3 N(1/2m
ideal gas heat capacity relation
Cp=Cv+R
gamme = Cp/Cv
ideal gas relation to U
PV=2/3 U
PV = U(gamma-1)
monotomic ideal gas heat capacity
C_v = 3/2 R Cp+5/2 R
hence
gamm = 5/3
diatomic ideal gas heat capacity
Cv=7/2R Cp=9/2 R
gamma =9/7
four steps to the Carnot cycle
isothermal expansion
adiabatic expansion
isothermal compression
adiabatic compression
engine efficiency equation
e=WQ=Q1-Q2/Q1 = 1-Q2/Q1
alternative form of the engine efficiency equation for the carnot engine
e=1-T2/T1
entropy equation
S=Q/T
entropy of adiabatic expansion
entropy of adiabatic expansion is constant
S(V,T) = NKb[lnV+1/(gamma-1) lnT] +a
first and second law of thermodynamics written together
du=dq+dw
du = Tds+ (-)PdV
how many thermodynamic processes does a system with 2 degrees of freedom have and what are they
4 thermodynamic processes
du = Tds - PdV
dH =TdS + VdP Enthalpy
dF = -SdT - PdV Helmholtz free energy
dG = -SdT + VdP gibbs
what does enthalpy represent
the heat transfer at constant temperature
H=H(P,V) = U + PV
what does Helmholtz and Gibbs free energy describe
they describe processes at constant temperature
F=F(T,V) =U -TS
what is the decrease in the Helmholtz energy
It is the maximum amount of work that may be extracted from a system during an isothermal change
Delta F = Delat U - T(Delta) S
reactions go in which way to favour the Gibbs?
Reactions go to minimise the Gibbs, it is constant for a reversible process at constant Temperature and pressure
what is the gibbs used to determine
the equilibrium states for a system with several phases
coefficient of performance for a backwards engine
Tc/Th-Tc = heat out / workdone
approx. 10 for a backwards carnot engine e.g. fridge
coefficient of performance of a heat pump
COP = |Qc|/W = Qc/Qh-Qc
coefficient of performance for a carnot heat pump
COP = Tc/Th-Tc
Boyles law curve at different temperatures
at high temperatures isotherms approx. to boyles law curve. at lower temperatues the boyles law curve becomes distoreted.
liquids compressible?
liquids are pretty incompressible
what equation is a good approximation for O2 and N2
the ideal gas equation is good approximations for O2 and N2 because roomt T»Tc for these solutions
The Clausius -clapyron equation
dp/dT=1Delta(S)/Delta(V) = L/T(Delta)V
where L is latent heat (absorbed)
Delta S is the change in entropy from phase 1 to phase 2
equation for three phases to co exist
g1=g2=g3
liquid to vapour transient equation
dp/dT = L/ Tb(Vg-Vl)
where Tb is boiling temp
Vg is gas volume
Vl is liquid volume
how many constraints does the triple point have
it has three constraints often the entropy increases when changing phase with increasing T
why do liquids cool as they evaporate
they lose the more enegetic molecules
what is intermolecular potential energy characterised by
the equilibrium separation ro and depth of the well e
Van der Waals forces equation
(P+a/Vm^2)(Vm-b)=RT
what do a stand for in the van de waals equation
The parameter a allows for the long-range intermolecular attraction which serves to lower the observed pressure
what does b stand for in the van der waals equation
the parameter b can be viewed as an excluded volume in a gas due to the present of the molecules (i.e. due to hard core repulsion)
what are intermolecular forces proportional too
the number of neighbours and collision frequency so f^2
when does the van der waals equation break down
for temperatures below the critical temperature. it is only good for small constraints
the entropy change during melting
Delta S f= mLf/Tf
Nernest-simon formulation of the third law
if Delta S is the entropy change during any reversible isothermal process ina condensed system then Delta S tends to zero as the temperature goes to absolute zero
what is the order of phase transition
the order of phase transition is defined as the order of the lwest differential of the Gibbs function which shows a discontinuity at the transion
