Entropy and Potential Temperature Questions and Answers

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.