Autumn Term Thermal Flashcards
What’s the difference between System and Surroundings
System is what we are studying, Surroundings is what we’re not
Define a closed system.
No particle exchange between system and surroundings
Define Adiathermal.
No heat exchange allowed (thermally isolated)
Define adiabatic
Adiathermal and reversible (mostly used synonymously with adiathermal)
Define isothermal.
At constant temperature
Define isobaric.
At constant pressure.
Define isovolumic.
At constant volume.
Define phase (in reference to system).
A region within a system which is homogenous within well defined boundaries
Define Equilibrium.
Refers to a state without apparent change, allows functions of state to be defined.
Define an Extensive FoS.
A FoS that us proportional to system size.
Define an Intensive FoS.
A FoS that is independent of size.
Give an example of an extensive FoS.
Energy, volume
Give an example of an intensive FoS.
Pressure, Temperature
What are Functions of State (FoS) also known as?
Thermodynamic functions, thermodynamic variables.
What is the Zero-th law of thermodynamics?
If A and C are each in thermal equilibrium with B, then A and C are also in thermal equilibrium with eachother.
What are the 3 types of temperature scales?
Empirical, Thermodynamic, Statistical
What is an Empirical temperature scale?
One based on a physical material, e.g. volume of a dilute gas/ liquid
How is Celsius converted to Kelvin?
T(k) = T(c) + 273.15
What is the ideal gas equation?
pV=nRT
How many degrees of freedom does the ideal gas equation have?
2, since it contains 3 functions of state
What is the equation for mechanical work (dW)?
dW = F dx (force x change in distance)
What is the First Law of Thermodynamics?
Energy is conserved if heat is taken into account
What is the typical equation form of the First Law of Thermodynamics?
Define terms.
ΔE = ΔW + ΔQ
ΔW = Work done to system
ΔQ = Heat supplied to system
What is the differential form of the First Law?
dE = dW + dQ
How is the differential First law altered to include pressure and volume?
dE = -pdV + dQ
If x=x(y,z) is finite and single valued, how is the exact differential dx found?
dx = (∂x/∂y)z dy + (∂x/∂z)y dz
What rule for second order differentials holds for all FoS?
Both orders of partial differential are equal
e.g ∂2x/∂y∂z = ∂2x/∂z∂y
Do Functions of State always have exact differentials?
Yes because they are all finite and single valued
What is the reciprocal theorem?
(∂x/∂z)y = 1/ (∂z/∂x)y
What is the reciprocity theorem?
(∂x/∂y)z(∂y/∂z)x(∂z/∂x)y = -1
What is the ideal gas expansion equation for an Isothermal system?
pV = const
What is the ideal gas expansion equation for an Adiabatic system?
pVƔ = const
What does CV mean?
Heat capacity at constant volume
What does Cp mean?
Heat capacity at constant pressure
What equation relates the isovolumic and isobaric heat capacities? (for 1 mole of ideal gas)
Ɣ = Cp/CV = 1 + R/CV
For 1 mole of ideal gas, Cp-CV=?
R
What is the value of Ɣ for a mono-atomic gas?
5/3
What is the value of Ɣ for a di-atomic gas?
7/5
Is the typical ideal gas mono-atomic or di-atomic?
Mono-atomic
What is CV in terms of a differential?
CV = (∂E/∂T)V
For an ideal gas, (∂E/∂v)T = ?
0
What does C represent?
Heat capacity
What is C in terms of Q?
C=dQ/dT
What is R?
Molar gas constant, R=8.314 J⋅K−1⋅mol−1
What is the Joule Expansion?
Expansion of a gas into a vacuum upon the sudden lifting of a partition.
Is the Joule expansion reversible?
Why?
No, Too many gas particles
What is the Kelvin definition of the 2nd law of thermodynamics?
No process is possible whose sole result is the complete conversion of heat into work
What is the Clausius definition of the 2nd law of thermodynamics?
No process is possible whose sole result is the transfer of heat from a colder to a hotter body.
How do the two 2nd law definitions finish this sentence:
'’No process is possible whose sole result is the …..’’ ?
Kelvin: No process is possible whose sole result is the complete conversion of heat into work.
Clausius: No process is possible whose sole result is the transfer of heat from a colder to a hotter body.
What is the name for a cyclic process that (partially) converts heat into work?
heat engine
What’s different about Joule Kelvin expansion compares to Joule expansion?
It’s constrained, e.g partition lifted is over a very small connector between chambers
Loosely, how does a heat engine work?
A working substance (assuming here ideal gas) interacts with two heat reservoirs at temps Th and Tl where Th > Tl.
Heat Qh is obtained from Th and Ql is passed onto Tl.
The work output is then W = Qh - Ql
What does the Carnot Cycle look like?
What are the four stages of the Carnot cycle?
A -> B isothermal expansion (top left line)
B -> C adiabatic expansion (top right)
C -> D isothermal compression (lower right)
D -> A adiabatic compression (lower left)
In the instance of the Carnot cycle, W represents what?
Work done by the system
(NOT on the system)
What does Qh represent in relation to the Carnot cycle?
Heat absorbed by the system
What does Ql represent in relation to the Carnot cycle?
Heat released by the system
If the Carnot cycle is done in reverse, A -> D -> C -> B -> A, what is it?
Heat pump / refrigerator.
Collects heat from the lower temp and delivers it to the higher temp
How is efficiency defined for a heat engine?
efficiency = η = W/Qh
The ratio Qh/Ql is equal to?
Th/Tl
Efficiency of a heat engine is defined as, η = W/Qh, how can this be written specifically for a Carnot engine in terms of T?
ηcarnot= (Th-Tl)/Th
What is Carnot’s Theorem?
Of all heat engines working between two given temps, none is more efficient than a Carnot engine
What is the general efficiency of a refrigerator defined as?
ηref=Ql/W
which is heat extracted over work input
Refrigerator efficiency is defined as ηref=Ql/W, how can Carnot refrigerator efficiency be written?
ηcarnot-ref=Tl/(Th-Tl)
How is Carnot’s theorem extended to reversible engines?
’ All reversible engines have the same efficiency as that of a Carnot engine’ which is then more efficient than any other heat engine.
How does thermodynamic temperature work as a measurement?
From a reference temp Θ1, run a reversible heat engine between this and temp to measure. Amount of heat exchanged defines Θ2.
Θ2=Θ1(Q2/Q1)
Why is the thermodynamic temperature scale important?
Conceptually it’s important to have a definition of temp which isn’t dependent on any material property, just on the
thermodynamic notion of reversibility.
What differential defines thermodynamic entropy?
dS = đQrev/T
What does the symbol đ
mean for a differential?
Not an exact differential
What is the integral definition of entropy?
S(B)-S(A) = integral from A to B of dS
(a is lower bound)
S represents what in thermodynamics?
entropy
S is defined via it’s differential so can vary by……
A constant
S is a/an _________ differential
Exact
What is the 3rd statement of the 2nd Law? (Clausius Inequality)
Entropy of an isolated system always increases
Can entropy decrease?
No, never
By the first law, dE = dQ -pdV, how can this be altered to include entropy?
dE = TdS - p dV since dS = dQ/T
By subbing S into the 1st law of thermodynamics, what do we gain?
The inexact differential for Q is removed and we can better manipulate the equation
If a system undergoes phase change from phase 1 to phase 2 at temperature T, what is the entropy change between phases?
(S2-S1) = L/T where L is latent heat supplied to change phase
How can Cp and CV be rewritten using S?
Cp=T(∂S/∂T)p
CV=T(∂S/∂T)V
When written in terms of entropy, how do the constant volume and constant pressure heat capacities vary?
Both are the same T(∂S/∂T) differential just with either p or v held constant accordingly
What energy, heat and temperature is involved in boiling a kettle?
Electric energy W is turned into heat Q that raises temperature T
When T isn’t constant, how can dQrev be written?
dQrev = Cdt where C is heat capacity
Define enthalpy (equation)
enthalpy, H = E + pV
What letter represents enthalpy?
H
What letter represents Helmholtz Free Energy?
F
Define Helmholtz Free Energy (equation)
Helmholtz Free Energy, F=E-TS
How are Helmholtz Free Energy and Gibbs Free Energy related?
F=E-TS
G=E-TS+pV
Therefore G=F+pV
What letter represents Gibbs Free Energy?
G
Define Gibbs Free Energy (equation)
Gibbs Free Energy, G=E-TS+pV
For the properties; Enthalpy, Helmholtz Free Energy, and Gibbs Free Energy, a differential form can be found - how is this simplified?
Each contains E, so by substituting for dE=TdS - pdV some terms will cancel
For a fixed temperature and volume, what is dF?
0, since dF relies on dT and dV
What is the Gibbs-Helmholtz equation for energy?
E = F-T(∂F/∂T)V
What ‘chart’ can be used to find the Maxwell relations?
How is the ‘chart’ used to find Maxwell’s relations?
From a gap between letters, circle one way where last value is held equal then circle the other. If the line is crossed, that derivative is negative e.g.
What is
R
What does βp represent?
isobaric expansivity, the fractional volume increase with temperature at a fixed pressure
What does KT represent?
Isothermal compressibility, the fractional volume decrease with pressure at fixed T
What is isothermal compressibility? What symbol does it have?
The fractional volume decrease with pressure at fixed T, KT
What is isobaric expansivity? What symbol does it have?
Fractional volume increase with temperature at fixed pressure, βp
What states does this equation hold for?
All, solid, liquid and gas
If entropy is constant, what does that mean for T and Q?
đQ = TdS = 0
What is KS?
Adiabatic compressibility, fractional volume decrease with T when S is constant (e.g. no heat flow but reversible)
How does this equation lead to a ratio of Cp and CV ?
What is the equation for KT? What’s the reasoning behind this?
Fractional volume decrease, so -1/v
And its the decrease wrt to pressure so partial differential of V to p, and T is fixed!
What’s the equation for βp?
Isobaric expansivity
For an ideal gas, does temperature change during Joule expansion?
NO
For real gas, does temperature change during Joule Expansion? Which way?
Yes, and for most gases it cools down
What differential defines the Joule expansion coefficient αJ?
Why is energy held constant for the Joule Expansion coefficient, αJ?
Because energy can’t change in a closed system, which the Joule expansion is.
If, for Joule expansion, Heat and work supplied by the process = 0 , enthalpy is ______?
Conserved
What is the Joule-Kelvin expansion coefficient,αJK?
Rate of change of T wrt pressure, holding enthalpy constant
What sign does the Joule kelvin expansion coefficient, αJK, typically take?
negative at high pressures (heating for p2<p1) and positive for low pressures
How to you get from
1) reciprocity theorem to turn differential into 2 that contain H
2) divide dH = Tds +Vdp by dp to substitute for (∂h/ ∂p)T
3) Use Cp=( ∂H/ ∂T)p to sub in
4) use maxwell relation to get final differential in terms of t and v
The Clausius inequality says dS≥ ?
How is availability defined?
A = E - T0S + p0V
where t0 and p0 are temp and pressure of surroundings that system is in contact with rather than the system itself
For a reversible process, dA ≤ ?
0
In Thermal isolation, with fixed volume dA = ?
dE
In thermal isolation, with fixed pressure, dA = ?
dH
For fixed T=T0 and fixed V, dA = ?
dF
For fixed T=T0 and fixed p=p0, dA = ?
dG
At equilibrium, dA = ?
0
Is availability a function of state?
no, nor a thermodynamic potential
In phase equilibrium, the specific Gibbs free energy is….?
The same for all co-existing phases
What is specific Gibbs free energy?
Gibbs free energy, G , per unit mass, M , = g
What is the Clausius Clapeyron relation for transitions between two phases?
where L = latent heat, l= specific latent heat
What is the 3rd law of thermodynamics?
As a system approaches absolute 0, all processes cease and the entropy of the system approaches a minimum value (zero)
As T approaches zero, what happens to the constant volume heat capacity CV?
It tends to 0
Demagnetisation leads to…..
Cooling
Adiabatic demagnetization is approximately what thermal process?
Joule-Kelvin Expansion
