Entropy and Potential Temperature Questions and Answers

Answer: C

The first two statements are correct, but reversible adiabatic ascent generates no entropy at all, which is precisely why potential temperature is conserved along it. Entropy generation requires irreversibility, whether from mixing, friction or heat transfer across a finite temperature difference. Recognising which processes are reversible is the whole content of the distinction. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: D

Irreversible mixing increases entropy rather than conserving it, so the last pairing is wrong. The other three correctly state the conditions under which each quantity is conserved. Assembling the conserved quantities alongside the conditions each requires is the most compact summary of atmospheric thermodynamics available.

Answer: A

The temperature falls as the parcel expands and does work on its surroundings, which is precisely why potential temperature was defined in the first place. Potential temperature, entropy and mixing ratio are all conserved provided no condensation occurs. Distinguishing the quantities that survive an adiabatic ascent from those that do not is what makes a thermodynamic diagram usable. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: B

Latent heat released by condensation raises the potential temperature of the parcel, moving it to a higher isentropic surface than the calculation assumes and invalidating the trajectory. Diabatic trajectory calculations are needed wherever cloud is present. This is the principal limitation of the isentropic method and the reason it is used mainly in the drier stratosphere. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: C

Because entropy is a function of potential temperature alone for an ideal gas, the two descriptions coincide and the surfaces are called isentropic. Adiabatic parcels are confined to them. Isobaric, isopycnal and isothermal surfaces are defined by pressure, density and temperature respectively, and each is useful for a different purpose.

Answer: D

Potential temperature requires dry adiabatic motion, equivalent potential temperature survives condensation as well, and potential vorticity additionally requires the absence of friction. The three form a hierarchy of increasing generality and increasing restrictiveness in different respects, and knowing which applies to a given situation is what makes each usable as a tracer. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: A

Potential temperature increases slowly through the troposphere and very rapidly through the stratosphere, so the isentropic surfaces are widely spaced below and tightly packed above. That packing is the strong stratospheric stratification. It is also why potential vorticity, which is inversely proportional to the isentropic layer thickness, is so much larger in the stratosphere. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: B

In isentropic coordinates the potential vorticity is the absolute vorticity divided by the mass per unit area between two neighbouring isentropes, so a thin layer implies a large value. This is why the strongly stratified stratosphere has such high potential vorticity. Stretching a column between two isentropes therefore reduces its potential vorticity unless the vorticity increases correspondingly, which is the shallow water result in another guise.

Answer: C

Bringing every parcel adiabatically to a common reference pressure removes the effect of its current height, so parcels sampled at 900 and 500 hectopascals can be compared on equal terms. That is exactly what an air mass label requires. Actual temperature compares samples at the same pressure adequately but fails entirely across levels, and humidity requires the separate moisture variables. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: D

Surface values near 290 kelvin rise to about 350 at the tropopause, so the troposphere spans roughly sixty kelvin of potential temperature. The stratosphere then spans several hundred more within a comparable depth, which is what makes its isentropes so tightly packed. The actual temperature range of 250 to 290 is a quite different quantity.