Explanations and Definitions Flashcards
thermal equilibrium
If there is no net flow of thermal energy between two physical systems
zeroth law
allows us to determine if two systems are in thermal equilibrium
exact differential
path independent
i.e. dU
inexact differential
path-dependent and relate to irreversible processes
i.e. δQ and δW
isothermal process
Temperature does not change
isobaric process
Pressure does not change
Isochoric process
Volume does not change
the link between the first law and Bernoulli’s equation
they are identical if there is no work, heat and no change in internal energy
the significance of the 2nd law in modern physics
the second law breaks the symmetry in Newtonian mechanics, quantum mechanics, electrodynamics and relativity.
it gives the concept of an ‘arrow of time’
carnot cycle PV diagram
see notes for PV diagram
1 -> 2 isothermal heat absorption Q(in)
2 -> 3 adiabatic expansion
3 -> 4 isothermal heat loss Q(out)
4 -> 1 adiabatic compression
kelvin Planck form of the 2nd law
it is impossible to construct a device that operating in a cycle will produce no other effect other than the conversion of heat into work
Clausis form of the 2nd law
it is impossible to construct a device that operating in a cycle produces no other effect than the transfer of heat from a colder body to a hotter body
kelvin planck and clausis statement of the second law
are equivalent
carnot’s theorem
no engine operating between two thermal reservoirs can be more efficient than a reversible engine operating between reserviors
consequences of carnot’s theorem
The efficiency is independent of the working substance and internal workings of the engine and solely dependent on the reservoir temperatures.
Providing a means to define an absolute temperature scale
the corollary to carnot’s theorem
all Carnot engines operating between the same two temperature reservoirs have the same efficiency
the thermodynamic temperature scale
is the triple point of water
the operation of a heat pump
3 loops connected by 2 heat exchangers to take heat from the ground to heat up a house.
the significance of the clausius inequality
the purpose of the Clausius inequality is to introduce entropy
for a closed system, we always need to consider the entropy of the surroundings.
discuss the significance of entropy
the entropy increases for an irreversible process
the total entropy of the universe cannot decrease
local decreases in S are allowed
it is necessary to consider the surroundings for systems that are not thermally isolated
carnot cycle on a TS diagram
see notes
it is a square
adiabatic lines are vertical lines
and isothermals are horizontal lines
functions of state
U,S and V
conjugate variables
T and S
S is extensive and T is intensive
four common thermodynamic potentials
U,H,F and G
the use of the four common thermodynamic potentials
express a given derivative into a measurable quantity
the need for a third law of thermodynamics in terms of absolute values of entropy
what is the standard point s(0) and whether is it the same for an ideal case can be provided by the third law
van der waals forces give rise to
a potential which is repulsive at short distances, but attractive at longer distances
become pronounced at small volumes and negligible at large volumes.
define a throttling process
a process to regulate or restrict the flow of a fluid by using a porous plug.
inversion curve
connects the maxima of different isenthalps on a PT diagram where µ = 0
µ < 0 heating upon expansion
µ > 0 cooling upon expansion
the physical process of producing liquid nitrogen and other liquid gases
gases can be directly liquified by throttling.
the operation of a domestic refrigerator
four stages
- throttling
- evaporation
- compression
- condensation
sketch of a typical refrigerator cycle on a TS plot
see notes
sketch of a Rankine cycle on a TS plot
see notes
the operation of a Rankine cycle
state a: pump
state b: boiler
state e: turbine
state f: condenser
steam engines utilise
the Rankine cycle
gas turbines utilise
the Brayton cycle
Brayton cycle TS plot
see notes
Brayton cycle PV plot
see notes
brayton cycle can be maximised for
the output of work W - W(c)
rocket engine sketch
see notes
define a first-order phase change
will have a discontinuous first derivative of G.
Measurement of the specific heat capacity will show a discontinuity at the phase transition temperature
higher order phase changes
third-order phase transitions occur in ferromagnetics or superfluids.
S(T)
∂S/∂T)(P) = c(P)/T > 0 and c(P) is always positive so the gradient on either side of the transition is positive.
Nothing can be said of the curvature
G(T)
∂G/∂T)P = -S < 0 so the gradient is negative on either side of the transition
∂^2G/∂T^2)P =
-∂S/∂T)P = -c(P)/T < 0 so the plots are curved downwards on either side
sketch of S(T) and G(T)
see notes
significance of F = -k(B)TlnZ
the equation links macroscopic classical thermodynamic variables to statistical mechanics quantities
PV diagram guide
See diagram
TS diagram guide
See diagram
why is Gibbs free energy used to describe phase changes
at a phase transition, two phases co-exist at the transition temperature and the Gibbs free energy for each phase is the same.
G is preferred over F because it is appropriate to the more commonly-used isobaric conditions
why is C(P) greater than C(V) for fluids
most materials expand upon heating, so C(P) includes work done by the material against the surrounding atmosphere.
why can we usually only consider either C(P) or C(V) for solids
for solids, the expansion is relatively small and the difference between them can often be ignored
Einstein model of specific heat capacity
- assumes a simple cubic lattice of N atoms with interatomic potentials modelled by springs, so that atoms can be modelled as simple harmonic in 3 dimensions
- assumed that each oscillator has a single frequency of oscillaton
- assumed that the solid can be treated as 3N independent oscillators
extensive thermodynamic variable
Variables that scale proportionally system size such as total mass or volume
throttling process
the rapid expansion of a fluid flowing through a restriction from a high-pressure region to a low pressure region, conducted under adiabatic conditions
an experiment that uses the Joule-Kelvin coefficient to determine whether a gas is well-described by the ideal gas law
porous plug experiment
porous plug experiment
throttling a high-pressure gas through a restriction in a pipe. The temperature drop across the restriction is measured. As the joule-kelvin coefficient is zero, there should be no temperature drop.
adiabatic
ΔQ = 0, exchanges no heat with its surroundings
blackbody
an object that perfectly absorbs all radiation that falls on it regardless of wavelength
Re radiates at energies characterised by a black body distribution
modern-day use of the Brayton cycle
used in jet turbines, for propulsion
why is the Debye model an improvement on the Einsten model
- allows a spectrum of excitation frequencies rather than the single frequency assumed by Einstein
- uses the concept of phonons, or coupled oscillations rather than the independent oscillations of the Einstein model.
- correctly predicts the low temperature T^3 dependence of heat capacity that is seen experimentally for simple solids.
Equipartition of energy
the thermal energy of an atomic or molecular system will be uniformly distributed between each ‘degree of freedom’ each of which accounts for energy 1/2 k(B)T
how does the equipartition of energy lead to differences in thermodynamic calculations for monatomic and diatomic gases
in monatomic systems, thermal energy is distributed between three degrees of freedom.
for diatomic molecules, there are also vibrational and rotational degrees of freedom to consider.
heat exchanger
enables the transfer from a hot material to cold material without the two materials physically mixing.
Heat pumps
operate similarly to refrigerators, taking some work to transfer heat from a cold body to a warmer body.
how to determine temperature from infrared intensity
Stefan-Boltzmann law on the formula sheet alongside the spectral density given by the Planck distribution, produces a unique curve that is only a function of T.
isentropic
where ΔS = 0
adiabatic process, where there is no transfer of heat ΔQ = 0.
It is also a reversible adiabatic process.
the kelvin temperature scale
is defined with respect to 273.16K
which is the triple point of pure water
which specifies a unique pressure and temperature which can be easily replicated in a lab
the scaling ensures that 1K is equivalent to 1 degree C.
The Joule-Kelvin process
a throttling process that is isenthalpic ΔH = 0. The gas is forced through a restriction or throttling valve in a lower-pressure region.
heat engine diagram
see notes
warm body
engine -> w
cold body
refrigerator diagram
see notes
warm body at T(1)
engine <- W
cold body at T(2)
How do we determine the one-particle partition function
by considering the Schrodinger equation for a particle in a box, which produces quantised energy levels that derive from standing wave solutions with nodes at the box walls.
Gibbs paradox is solved
if the particles are assumed to be
indistinguishable
The Gibbs Paradox
S is expected to be an extensive property but is not extensive in the above result.
