Entropy and Potential Temperature Questions and Answers

Answer: A

For an ideal gas the specific entropy equals the specific heat at constant pressure multiplied by the natural logarithm of the potential temperature, plus an arbitrary constant. This single identification is what makes potential temperature so central to atmospheric thermodynamics, because it means that a surface of constant potential temperature is a surface of constant entropy and that adiabatic reversible motion is confined to such a surface. The arbitrary constant is harmless because only entropy differences ever enter a physical calculation.

Answer: B

A reversible adiabatic process exchanges no heat and generates no entropy internally, so the entropy of the parcel is conserved and its potential temperature is therefore constant. Mixing, heating and evaporation all change the entropy. The identification of adiabatic with isentropic requires the reversibility, which is why the pseudo-adiabatic process of saturated ascent with precipitation removal is adiabatic but not isentropic.

Answer: C

Because entropy is a function of potential temperature alone for an ideal gas, the two descriptions are equivalent and the surfaces are called isentropic. Adiabatic parcels are confined to them, which is what makes them so useful for visualising three dimensional flow. Isobaric, isopycnal and isothermal surfaces are defined by pressure, density and temperature respectively. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: D

Conservation of potential temperature confines an adiabatic parcel to its isentropic surface, so its vertical motion is determined entirely by the slope of that surface and the horizontal wind along it. This is why isentropic analysis makes vertical motion visible as flow across the height contours of the surface. Diabatic processes are what allow a parcel to change surfaces. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: A

Potential temperature increases both upward and equatorward, so a surface of constant value must rise as one moves poleward. Typical slopes are of order one in a thousand, far gentler than the frontal surfaces embedded within them. Air flowing poleward along such a surface therefore ascends, which is the isentropic statement of warm advection producing ascent. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: B

Because the surfaces rise polewards, a parcel confined to one and moving polewards must rise. Equatorward flow correspondingly descends. This gives the same answer as the omega equation but by a much more direct route that also displays the trajectory the parcel actually follows, which is why isentropic analysis remains a valued diagnostic tool. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

Answer: C

An isentropic chart contours the pressure or the Montgomery streamfunction on a surface of constant potential temperature, and the flow across the pressure contours shows the vertical motion directly. Constant pressure charts contour height on a pressure surface, which is the complementary construction. Both display the same three dimensional field from different slices. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: D

The Montgomery streamfunction combines the geopotential with the product of the specific heat and the temperature, and its gradient on an isentropic surface gives the geostrophic wind there. It plays exactly the part that geopotential plays on an isobaric surface. Introducing it is what makes the isentropic geostrophic relation as simple as the isobaric one. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: A

Confining the trajectory to a two dimensional surface reduces the computation enormously while automatically capturing the vertical motion through the slope. Isentropic trajectory models were the standard tool before full three dimensional computation became affordable and remain useful for tracer studies. The surfaces are of course not horizontal, which is precisely what carries the vertical information. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

Answer: B

Condensation, radiation and turbulent mixing all change the potential temperature of a parcel and move it to a different surface, so trajectories through cloud cannot be computed by this method. Adiabatic motion along the surface and horizontal advection within it are precisely what the method represents correctly. The Coriolis force is included through the wind field. Framing the question as which quantity the change acts upon makes the answer follow without calculation.