Entropy and Potential Temperature Questions and Answers

Q: Which quantity does the Earth export to space?

The Earth receives energy in a small number of high energy solar photons and emits the same energy as a much larger number of low energy infrared photons, so it exports far more entropy than it receives. Energy is exported at the same rate it is received in the long term mean. That entropy export is what permits the maintenance of the ordered structures of the circulation and of life. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Q: Which principle has been proposed to constrain the climate state?

Some authors have proposed that the climate system organises itself so as to maximise the rate of entropy production, which reproduces the observed poleward heat transport surprisingly well. The principle has no rigorous foundation and remains controversial. It is nonetheless an interesting example of an attempt to constrain a complex system by a variational argument rather than by solving its equations. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Q: Which quantity does the Carnot efficiency bound?

The Carnot efficiency, one minus the ratio of the cold to the hot absolute temperature, is the maximum fraction of the absorbed heat that any engine can convert into work. For the atmosphere with 300 and 250 kelvin it is about 17 per cent, against an observed conversion near 1 per cent. The gap reflects the irreversibility of the actual heat transfer. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Q: Which comparison does the atmospheric heat engine make?

About 240 watts per square metre are absorbed and about 2 watts per square metre appear as kinetic energy, giving an efficiency near 1 per cent against a Carnot bound of 17. The remainder is transferred irreversibly by radiation and turbulent mixing. The final option describes a balance that holds in the steady state rather than an efficiency. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Q: Which fraction of the total potential energy is available?

Lorenz showed the available portion to be around 0.5 per cent of the total, because most of the mass is already close to its lowest attainable arrangement. Even that small fraction is about ten times the kinetic energy of the general circulation. The calculation corrects the intuition that a large reservoir must imply a large usable supply.

Q: Which rearrangement defines the reference state for that calculation?

The reference state is obtained by rearranging the mass adiabatically until every isentropic surface is horizontal, which minimises the total potential energy at fixed entropy distribution. The difference between the actual and reference potential energies is the available portion. Isothermal or fully mixed states would change the entropy and are therefore not reachable adiabatically. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Q: Which quantity is conserved during that adiabatic rearrangement?

Adiabatic rearrangement moves parcels without changing their potential temperature, so the mass contained between any two isentropic surfaces is preserved. Temperature and pressure both change as the parcels are moved. The construction is a thought experiment rather than a physical process, but it gives a well defined and computable reference against which the actual state is measured. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Q: Which four reservoirs appear in the Lorenz energy cycle?

Lorenz divided both available potential energy and kinetic energy into zonal mean and eddy parts, giving four reservoirs connected by conversion terms. The dominant pathway runs from zonal available potential energy through the eddy form to eddy kinetic energy and finally to zonal kinetic energy. Mapping the observed magnitudes onto that diagram summarises the general circulation compactly. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Q: Which conversion dominates the observed cycle?

The baroclinic conversion driven by the poleward eddy heat flux is the largest term and is the first step of the dominant pathway. It is followed by conversion to eddy kinetic energy and then, during barotropic decay, to zonal kinetic energy. Direct conversion from zonal to eddy kinetic energy is small and often of the opposite sign.

21.

Which quantity does the Earth export to space?

A.Entropy, at a rate exceeding that received from the sun
B.Energy, at a rate exceeding that received from the sun, which is what allows the planet to cool progressively
C.Neither
D.Angular momentum, which is transferred to space by the escape of atmospheric molecules from the exosphere above

Answer: A

The Earth receives energy in a small number of high energy solar photons and emits the same energy as a much larger number of low energy infrared photons, so it exports far more entropy than it receives. Energy is exported at the same rate it is received in the long term mean. That entropy export is what permits the maintenance of the ordered structures of the circulation and of life. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

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22.

Which principle has been proposed to constrain the climate state?

A.The equipartition of energy among the available degrees of freedom of the molecules within the atmosphere
B.Maximum entropy production
C.Minimum energy, which requires the atmosphere to adopt the configuration with the lowest potential energy possible
D.Conservation of entropy

Answer: B

Some authors have proposed that the climate system organises itself so as to maximise the rate of entropy production, which reproduces the observed poleward heat transport surprisingly well. The principle has no rigorous foundation and remains controversial. It is nonetheless an interesting example of an attempt to constrain a complex system by a variational argument rather than by solving its equations. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Discuss in Forum

23.

Which quantity does the Carnot efficiency bound?

A.The entropy production
B.The rate at which a heat engine is able to complete its cycle when operating between two fixed temperatures
C.The fraction of heat convertible into work
D.The total quantity of heat that a system is able to absorb from a reservoir at a given temperature per second

Answer: C

The Carnot efficiency, one minus the ratio of the cold to the hot absolute temperature, is the maximum fraction of the absorbed heat that any engine can convert into work. For the atmosphere with 300 and 250 kelvin it is about 17 per cent, against an observed conversion near 1 per cent. The gap reflects the irreversibility of the actual heat transfer. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Discuss in Forum

24.

Which comparison does the atmospheric heat engine make?

A.The temperature of the surface against the temperature of the stratosphere at the level of the ozone maximum
B.Rainfall against evaporation
C.The kinetic energy of the general circulation against the kinetic energy dissipated by friction at the surface
D.Absorbed solar energy against generated kinetic energy

Answer: D

About 240 watts per square metre are absorbed and about 2 watts per square metre appear as kinetic energy, giving an efficiency near 1 per cent against a Carnot bound of 17. The remainder is transferred irreversibly by radiation and turbulent mixing. The final option describes a balance that holds in the steady state rather than an efficiency. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Discuss in Forum

25.

Which reservoir supplies the atmosphere with available potential energy?

A.Differential heating between low and high latitudes
B.The kinetic energy of the zonal mean flow, which is converted into potential energy as the eddies decay away
C.Frictional dissipation
D.The latent heat carried poleward by the eddies, which is released as the air ascends within the storm tracks

Answer: A

Heating in the tropics and cooling at high latitudes continually creates the horizontal temperature gradient from which available potential energy derives, and that is the source term for the whole Lorenz cycle. Friction is the sink at the other end. Latent heat release is an important internal transfer rather than the ultimate source.

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26.

Which fraction of the total potential energy is available?

A.Essentially all of it, because any horizontal temperature gradient could in principle be entirely removed
B.About half of one per cent
C.About half, since the atmosphere is close to the point at which convection would begin throughout the column
D.About ten per cent

Answer: B

Lorenz showed the available portion to be around 0.5 per cent of the total, because most of the mass is already close to its lowest attainable arrangement. Even that small fraction is about ten times the kinetic energy of the general circulation. The calculation corrects the intuition that a large reservoir must imply a large usable supply.

Discuss in Forum

27.

Which rearrangement defines the reference state for that calculation?

A.Complete mixing
B.Rearrangement to the state of minimum entropy, which is the configuration that the system would adopt naturally
C.Adiabatic rearrangement to a horizontally uniform stratification
D.Isothermal rearrangement, in which every parcel is brought to the same temperature throughout the atmosphere

Answer: C

The reference state is obtained by rearranging the mass adiabatically until every isentropic surface is horizontal, which minimises the total potential energy at fixed entropy distribution. The difference between the actual and reference potential energies is the available portion. Isothermal or fully mixed states would change the entropy and are therefore not reachable adiabatically. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Discuss in Forum

28.

Which quantity is conserved during that adiabatic rearrangement?

A.The temperature of each individual parcel, which must remain unchanged as the rearrangement is carried out
B.The pressure
C.The kinetic energy of the flow, which is not affected by any rearrangement of the mass within the atmosphere
D.The mass between each pair of isentropic surfaces

Answer: D

Adiabatic rearrangement moves parcels without changing their potential temperature, so the mass contained between any two isentropic surfaces is preserved. Temperature and pressure both change as the parcels are moved. The construction is a thought experiment rather than a physical process, but it gives a well defined and computable reference against which the actual state is measured. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Discuss in Forum

29.

Which four reservoirs appear in the Lorenz energy cycle?

A.Zonal and eddy available potential energy and zonal and eddy kinetic energy
B.Internal potential kinetic and latent energy, considered for the atmosphere as a whole rather than by component
C.Radiative latent sensible and kinetic energy
D.Available potential energy divided among the four seasons at each latitude of the globe throughout the year

Answer: A

Lorenz divided both available potential energy and kinetic energy into zonal mean and eddy parts, giving four reservoirs connected by conversion terms. The dominant pathway runs from zonal available potential energy through the eddy form to eddy kinetic energy and finally to zonal kinetic energy. Mapping the observed magnitudes onto that diagram summarises the general circulation compactly. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Discuss in Forum

30.

Which conversion dominates the observed cycle?

A.Latent heat directly into zonal kinetic energy through the release of buoyancy within tropical convection
B.Zonal to eddy available potential energy
C.Zonal kinetic energy directly into eddy kinetic energy, with no potential energy being involved at any stage
D.Eddy kinetic to zonal available potential energy

Answer: B

The baroclinic conversion driven by the poleward eddy heat flux is the largest term and is the first step of the dominant pathway. It is followed by conversion to eddy kinetic energy and then, during barotropic decay, to zonal kinetic energy. Direct conversion from zonal to eddy kinetic energy is small and often of the opposite sign.

Discuss in Forum

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