entropy Flashcards
what is entropy, is it a path or state function
the flow of heat resulting in the system losing the capacity to do work,
state function
define entropy in equation form
deltaS = Sb - Sa =
intergral of change of heat over Temp
how does the flow of heat affect the capacity of doing work
the flow of heat reduces the capacity to do work as dU = dbarQ + dw
what is dbarQrev at constant temp
dbarQrev = TdS
what about entropy is an equilibrium condition
dS = dbar q / T because deltaS= integral dqrev / T only holds for reversible path
what are the conditions for a spontaneous process
dbarq dbarq/T for all observable processes
what is general definition of equilibrium
dS = dbarq/T
what are the conditions of an obseravable change
dS>0 as dS>dbarq/T
what happens when a spontaneous change occurs in an isolated system (second law of thermodynamics)
this will produce a states of higher entropy until reaches a max value at which the system will be in equilibrium and entropy will remain constant at max value.
how do you prove entropy is a state function
consider perfect gas where dU=dbarqrev - PdV if system only does PV work
for one mole of perfect gas: dU = CdT and as P=RT/V
so dS=dbarqrev/T = Cdt/T + RdV/V which intergrates tp:
Sb - Sa = Cln(Tb/Ta) + Rln(Vb/Va)
showing dbarqrev/T is exact differential and that S is state function for a perfect gas
how to show entropy change of reversible expansion of perfect gas
deltaU = q + w,
perfect gas U independent of volume deltaU = 0 so
q = -w
gas expands pressure drops, external pressure continuously adjusted so that p = pex + dP expansion carries out reversibly doing max work and
-wrev = integral PdV
p=nRT/V
-wrev = nRT integral dV/V = nRTln(Vb/Va)
deltaS = qrev/T
= nRTln(Vb/Va)
for reversibly deltaSoverall=0
= qrev/T - qrev/T
what is entropy of an irreversible expansion of a perfect gas
irreversible expansion of a perfect gas into a vacuum no work done so deltaSoverall no longer 0
deltaS=nRln(Vb/Va) ,
gas does so work q = -w = 0 so no heat absorbed
deltaS = nRln(Vb/Va) + 0/T
Vb>Va total entropy of system and surroundings will have increased,
entropy change in gas is same for reversible and irreversible expansion so investigate surroundings before determining if rev or not.
how is entropy change when heat flows from Th to Tc
dS = (-dbarq/Th) + (dbarq/Tc) dS = dbarq((Th-Tc)/ThTc)
what are the fundamental thermodynamic equations
when volume can change, tendency to maximise S(V) predicts expansion of gases
particle numbers change max S(N) predict change in composition
energy can change, max S(U) predict tendency for heat flow
if all can change fundamental TD equation for entropy S = S(U,V,N)
what are the 2 factors that drive chemical systems to equilibrium
tendency to minimise their energy
tendency to maximise entropy
how do you show entropy as a function of pressure and temperature
S = Sb - Sa = nRln(Vb/Va)
P inversely proportional to V of perfect gas under isothermal conditions
S=Sb-Sa = -nRln(Pb/Pa)
S0 = entropy of perfect gas at 1atm
S=S0 - Rln(P/P0) =
=S0 - Rln(P/1) = S0 - Rln(P)
shows that pressure increases as entropy decreases
show Cv and Cp in terms on dbar-q-rev
express the entropy terms
Cv = (dbar-q-rev/dT)v Cp = (dbar-q-rev/dT)p
as dS= (dbar-q-rev / T)
dS=(Cv/T)dT
dS=(Cp/T)dT
integrate to
deltaS = C ln(Tb/Ta)
if So is entropy at 0 K entropy at T:
S(T) = So + integral Cp/T dT
what is the third law of thermodynamics
what is common for most pure substances?
the entropy of all perfect crystals is zero at the absolute zero of temperature
form perfect crystals at low temp so assume So = 0
describe the entropy for the states of matter
solids - molecules / atoms tightly bound together so entropy is low
gases - molecules free to move in large volumes so entropy is high
liquids - intermediate in their properties
how does entropy change during vaporisation
molecules leave state of modest freedom to one of high freedom so positive entropy change,
deltavapS = qrev / T
= deltavapH/T
when got box A and box B where box A is half-filled while B is full-filled how is the entropy change per mole between the states found
which definition of entropy does this lead to
probA/probB = (Va/Vb)^M ln(probB/probA) = Mln(Vb/Va) 1mol gas Sb-Sa = Rln(Vb/Va) M = Na Sb-Sa = (R/Na)ln(ProbB/ProbA)
S = Kb ln(omega) Kb = R/Na omega = num microstates
when counting events and objects are indistinguishable how can number of permutations (omega) be calculated
(N!/n1!n2!…nt!) = omega
N = number of trails
n = results
N!/n!(N-n)!
what is a macrostate
macroscopic observable or controllable which can perform experiment in which we vary or measure volume or density N/V of the system
what is a microstate
individual snapshots that are counted and equally probable which macrostates are made up of. probability of observing a particular macrostate is proportional to how many microstates it has
how does the value of omega link to diffusion and the probable layouts of energy distribution
Diffusion: larger omega predicts diffusion as S=Kbln(omega) and link entropy in terms of set of probabilities
energy: having particles spread over more energy levels is most probable as has largest omega and corresponds to max number of microstates
what is deltaS for energy distributions when in thermodynamic equilibrium
deltaS = -K ln(ni/n0)
or = thermalEi/T
ni/n0 = e^-thermalEi/kT
(Boltzmann distribution)
