Week 1? Flashcards
Extensive properties
Depends on amount
Intensive property
Independent of amount
Determine whether extensive
- Additive e.g if property is V^2, (V^a)^2 + (V^b)^2 should = (V^a + V^b)^2
- Proportional to size of quantity of substance
Determine whether intensive
- Does not add up when part of system are combined
- Constant regardless of substance size
Define state
Set of conditions (T, P,V) that’s fully describe system at a given moment
Equilibrium
All macroscopic properties of a system are well-defined and remain constant over time
Response function
how a system reacts to changes in external variables
Temperature
Measure of average kinetic energy of particles in a system
function of state
Any thermodynamic property that depends only on the state of the system and not the history of how it reached that system
Reciprocity theorem
Response to perturbation is symmetric -> one variable affects another
Reciprocal theorem
Response of one system to external force is symmetric
Fundamental relation
Equation that relates internal energy to state variable
System
Portion of universe being studied
Reversible
- Infinitely slow and at thermodynamic equilibrium at every stage
- Can be exactly returned to original state by reversing process
Features of reversible
- No entropy generation
- Infinitely slow
- Idealised
Quasi static
- So slow that can be assumed to be in equilibrium at all times
Features of quasi static
- Slow and continuous
- No sudden changes
- Approximates reversible
Irreversible
Cannot be reversed by an infinitesimally small change in external conditions
Features of irreversible
- Entropy generation
- Not reversible
- Energy dissipated
bulk modulus
Property that measures a material’s resistance to uniform compression
Formula bulk modululs
K = -V * ΔP/Δ V
Improper differentials:
- Discontinuous e.g. phase transition
- Sharp corners/edges e.g. critical temp/pressure
- Singularities e.g. compressibility near critical point
- Path dependent
Specific properties
Extensive property/mass
Relate density and volume
Density = 1/volume
Cycle
System that returns to original state
Celsius to Fahrenheit
X1.8 +32
Fahrenheit to Rankine
+459.67
Rankin to Kelvin
X1.8
Kelvin to Celsius
+273.15
Absolute temperature
K, R = start at zero
Absolute pressure
Actual pressure + gauge pressure
Atmospheric pressure
1 atm = 101.325 kPA
How to find conversion from Rankin to Kelvin
- both absolute zero (no y intercept needed)
- m = e.e.g freezing point in F/freezing point in C
=491.67/273.15 = 9/5
When saying “twice as hot”
Need to reference temperature scale or does not make sense
Relaxation time
Time needed to come to thermal equilibrium
~2minutes
Thermal expansion coefficient, β
(ΔV / V) / ΔT
What is room temperature?
25 Celsius
Boltzmann constant in J/K
1.381x10^-23
Boltzmann constant in L.atm/(mol.K)
0.0821
Cubic metres into litres
1 m^3 = 1000L
How to approach problems asking to compare e.g. number of moles in 2 rooms
Two simultaneous equations based on ideal gas law
- Find something to equate
- Rearrange to equate as e.g.Na = X Nb
What is a good estimate of average particle speed?
Vrms
Vrms formula
SQRT (3Kt)/m
NB Mass = Atomic mass/avogadro’s in GRAMS and Kb in KG -> need to convert and check SI units/dimension analysis
Which molecules move faster in gas in thermal equilibrium
= 1/2 m v^2 , so one with lowest mass
Pressure due to KE of particles
= Force over area, where force = rate of change in momentum
= Nmv^2 /V
Effusion
Gas molecules pass through tiny hole without collisions between molecules
Graham’s law of effusion
Rate of effusion ∝ 1/sqrt (M)
Change in velocity in x direction after particle collision
= -2 * velocity in x direction
(ΔV = Vf - Vi = -Vi - Vi = -2 Vi )
number of particles colliding with surface of area A
Pressure =force/area where force =rate of change in momentum and v = -2v due to collision
P = m2Nvbar/ (A Δt)
->rearrange for N
What is the miracle of thermodynamics?
Universality of thermodynamics
Extensive properties
V,n
Intensive properties
P, T
Examples of reversible reactions
Isothermal expansion/compression
Phase change at equilibrium
Examples of irreversible
- Spontaneous
- Free expansion (e.g Joule expansion)
-
Features of free expansion
- No external work
- No heat exchange (insulated)
- U constant
- Irreversible
- Entropy rise
Which are state functions?
U, H, S, G, A/F,
zeroth Law
If 2 systems are in THERMAL equilibrium with a third, then they are in equilibrium with each other
Which are important non state functions?
Heat, work
Negative sign for work
Work done on system i.e. compression
Positive sign for work
Work done by system i.e. expansion
Miracle of thermodynamics
Ability to describe thermodynamic behaviours of systems ignoring that they are made of molecules and focus on variables only
Boyle’s law
PV =constant
Charles’s Law
V/t = constant
Gay-Lussac Law
P/t = constant
Avogadros Law
V/n= constant
How to find isothermal work from isobaric?
- Work isobaric = P1 (V2-V1)
- Work isothermal. = nRT1 ln (V2/V1)
- Sub P1 = nRT1/V1 into 1
- Work isobaric = nRT/V1 ( V2 - V1) = nRT1(V2/V1 1) - Rearrange 3:
- ΔV = (Work isobaric/nRT1) +1 - Sub 4 into 2
- Work isothermal = nRT1 ln (Work isobaric/nRT1) +1
Calculate work from graph
Area under curve (down to x axis)
Microstate
Microscopic information about a state e.eg position and momenta of molecules
Macro state
Described by its macroscopic properties
- Many microstate configurations
What makes it possible to measure temperatures?
Zeroth law
Define thermometer
Working substance with measureable property - length, pressure etc, which changes in a regular way as substance becomes hotter/colder
Pressure at triple state of water
610.6Pa
Water freezing and boiling in Fahrenheit
32 and 212
function of state?
Only depend on its current thermodynamic state, not path
PV units for ideal gas law 8.314J/mol.K?
P = Pa
V = m^3 (i.e. litres/1000)
PV units for ideal gas law 0.0821 L.atm/mol.K?
P = atm
V = L
Find function of exact differential
- Verify exact by dx/dy = dy/dx
- Integrate e.g. dx/dy wrt y (or dy/dx wrt x)
- Compare integrand to e.g. dx in differential
- Integrate what is left wrt e.g. x
- State function
More insulating in series or parallel? Why?
- Better insulation in series as added as resistances
( Series = R1+ R2+…; 1/ Parallel = 1/R1 + 1/R2+….)
How to calculate heat current
Q/t = (kA ΔT)/d
D= thickness
Reduction in heat loss due to huddling in penguins
- Model penguins as cylinders
- Subsitiute r in terms of area (a = π r^2)
- Relate the 2 (heat loss penguin / heat loss cylinder*N)
- Should have 2 similar equations with extra factor of SQRT (1/N) on top ->factor out to have 1/4th root of N
Calculate gas pressure inside cylinder with piston
Pgas = Patm + mg/A
Convert bar to PA
1 bar = 100,000 Pa
Work for gas in cylinder with piston
W = F.d = (mg + Patm.A) * ( ΔV/A)
= ( mg/A + Patm) * ΔV
Way to compute work for adiabatic
Work = (P1V1 - P2V2)/(γ-1)
Where is heat in / out on PV
QH (in) top horizontal and left
QC (out) bottom horizontal and right
Which curve is higher I.E. more work on PV diagram - isothermal or adiabatic?
Isothermal
Is heat lost or gained during compression?
Lost
Efficiency
Work/Qin
Or Qin - Qout/ Qin
Define Newtons Law of Cooling
The hotter something is compared to its surroundings, the faster it cools down.
- the rate at which an object cools down is proportional to the difference between its temperature and the surrounding temperature.
Differential form of 1st law
First law for cyclical
W = U
Define heat capacity
amount of heat needed to raise the temperature of a substance by 1 degree Celsius (or 1 Kelvin).
Heat capacity formula
C = Q/ ΔT
Which is Qlow?
One for compression/pressure reduction
- decreased P and/or V
Which is Q high
One for expansion/higher pressure
Place of highest temperature on PV diagram?
Top left
Meaning of “1 unit mass” in question?
- 1kg of air contains n= 1/M moles
- M = molar mass e.g. 28.97g/mol for air
What is important to note in cycle heat calculations?
Isobaric or isochoric as changes heat equation used
