Lectures 1 & 2 Flashcards
what is an extensive property?
an extensive property depends on the amount of substance
e.g mass volume, enthalpy, entropy, internal energy, helmholtz energy, gibbs free energy
what is an intensive property?
an intensive property takes the same value irrespective of the amount of substance
e.g. temperature, pressure, density, viscosity, specificheat capacity, mole fraction, molar volume
what is a state function/ variable?
the value only depends on the current state of the substance. only takes into account the initial and final values
e.g. temperature, pressure, all energies (U,S,A,G,H)
what is a path function?
a path function depend on the history of the system by which the system has reached current state
e.g. work, heat
what is energy?
energy is the ability of a system to do work
what is heat?
heat is a form of energy associated with the movement of atoms and molecules in any material. the higher the temperqature of a material, the faster the atoms are moving, and hence the greater the amount of energy present as heat
what is the molecular interpretation of heat?
the transfer of energy that makes use of chaotic molecular motion
what is the notation for heat
δQ=T dS
where δQ is a path function and T dS
what is work?
work is the energy required to move an object against a force
what is the molecular intrepretation of work?
work is the transfer of energy that makes use of organised molecular motion
derive an expression for expansion/ compression work
dW= F dx
P=F/A
A dx = V
dW= -P dV
where δW is path function
how are changes in internal energy U achieved?
achieved by heating or cooling, or by doing work on the system or extracting work from the system
write an expression for the change in internal energy
ΔU= Q+W
write a statement of the first law?
the internal energy of an isolated system is constant
ΔU isolated = 0
what is the fundamental equation of internal energy
dU = T dS -P dV
derive the fundamental equation for internal energy
dU=δQ+ δW from the first law
δW= -P dV define expansion/compression work
δQ = T dS a relation between heat and entropy
therefore: dU = T dS -P dV
does the fundamental equation for internal energy apply for reversible or irreversible processes?
the fundamental equation for internal energy is a state function (only depends on the initial and final states) therefore it doesnt matter if the process is reversibl or irreversible. this is a general statement
how do you calculate internal energy for constant volume processes?
for a constant volume process
-P dV= 0
therefore we need to measure
ΔU=Qv
which we can gather from molecular information like the equipartion theorem and maxwell molecular velocity distribution
what is the equation for enthalpy?
H=U+PV
is enthalpy a state or path function
ΔH=Hfinal -Hinitial
therefore, enthalpy is a state function
derive an equation for the change in enthalpy
dH= dU+d(PV)
= T dS -P dV + P dV + V dP
dH= T dS + V dP
how would you measure and calculate ΔH?
ΔH is related to the heat supplied at constant pressure
ΔH=Qp
for an endothermic reaction ΔH>0
for an exothermic reaction ΔH<0
what is the second law in terms of entropy?
if an isolated system undergoes change, it will change in such a way that its entropy will increse or, at best, remain constant
S tot ≥ 0
what does spontaneous change mean?
spontaneous means it occurs with no need for external influence or driver
( no implication on the rate of the process, the process can be fast or slow)
how does spontaneous change affect entropy
the entropy of an isolated sytem increases in the course of spontaneous change
what is the entropy at equilibirum
ΔS tot = 0
the system is at a maxium in entropy, since direction of spontaneous change is to increase entropy
no entropy change
what does entropy relate
entropy is a quantity that relates heat absorbed from or delivered to a reservoir at a given temperature
dS = δQrev/ T
what is Qrev
Qrev is the energy (heat) transferred reversibly to the system at absolute temperature T
what is the total entropy?
the total entropy involves the system and its surroundings
dStot = dSsys + dSsurr ≥ 0
why does δQsurr= - δQsys
because the surroundings act as a heat source for the system
why are the surroundings unaltered by the heat loss
because the surroundings are arbitrarily large ‘infinite’ and therefore the heat exchanged is infinitesimal
if the surroundings are unaltered by the heat loss what does that mean for the entropy of the surroundings
dSsurr= δQsurr/Tsurr
derive dS≥ δQ / T
dStot = dSsys + dSsurr ≥ 0
∂Qsurr= -∂Qsys (surroundings act as heat source to the system)
dSsurr= ∂Qsurr/Tsurr (entropy of surroundings)
therefore,
dSsurr=- ∂Qsys/Tsurr (from above relation)
dStot = dSsys - ∂Qsys/Tsurr ≥ 0 (from above relation)
dSsys ≥ ∂Qsys/Tsurr
then, if the system is a thermal equilibrium with its surroundings Tsurr=Tsys=T
therefore, dSsys≥ δQsys / T
then we normall drop the ‘sys’ subscript to form the clausius inequality
dS ≥ δQ/T
what is the clausius inequality?
dS ≥ δQ/T
or
TdS -δQ ≥ 0
what is clausius inequality for macrocscopic quantities
ΔS≥Q/T
TΔS -Q ≥ 0
derive an equation for helmholtz free energy A
TΔS -Q ≥ 0 second law
@ specified T,V
Q= ΔU
TΔS -ΔU ≥ 0 by definition -ΔA
therefore
ΔA=ΔU -TΔS
ΔA(V,T)≤ 0
ΔA=A(T2,V2)-A(T1,V1)
what is the helmholtz free energy?
the helmholtz free energy A provides the direction of spontaneous change in processes where volume V and temperature T are independent (specified) variables
A=U-TS
what is the helmholtz free energy in terms of differentials
dA=dU-d(TS)
dU=TdS-PdV
dA=TdS-PdV-TdS-SdT
dA=-PdV-SdT
what is the gibbs free energy
the gibbs free energy G provides the direction of spontaneous change in processes where the pressure P and temperature T are independent (specified) variables
derive the gibbs free energy equation
TΔS -Q ≥ 0 second law
@ specified T,P
Q= ΔH
TΔS -ΔH ≥ 0 by definition -ΔA
therefore
ΔG=ΔH -TΔS
ΔG(P,T)≤ 0
ΔG=G(T2,P2)-G(T1,P1)
ΔG=0 if at equilibrium
ΔG< 0 if spontaneous
what is the gibbs free energy in terms of differentials
G=H-TS
dG=dH-TdS-SdT
dH=TdS+VdP
dG=TdS+VdP-TdS-SdT
dG=VdP-SdT
what is the entropy for real systems
absolute entropies for real systems re strictly positive
S>0 for real systems
what is ΔG at equilibrium?
0
what is ΔG during spontaneous change
less than 0
what does ΔG≤ 0 determine?
determines the direction of spontaneous change at given P and T
