Entropy and Potential Temperature Questions and Answers

Q: Which quantity is the specific entropy of an ideal gas proportional to?

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.

Q: Which process leaves the entropy of a parcel unchanged?

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.

Q: Which name is given to a surface of constant potential temperature?

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.

Q: Which motion do adiabatic parcels perform relative to those surfaces?

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.

Q: Which slope do isentropic surfaces have in mid-latitudes?

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.

Q: Which vertical motion does poleward flow along such a surface produce?

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.

Q: Which chart displays the pressure on an isentropic surface?

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.

Q: Which function plays the role of the streamfunction on an isentropic surface?

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.

Q: Which advantage does isentropic analysis have for trajectories?

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.

Q: Which process breaks the isentropic trajectory assumption?

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.

Which quantity is the specific entropy of an ideal gas proportional to?

A.The logarithm of the potential temperature
B.The absolute temperature itself, in the same way that the internal energy of an ideal gas depends upon it
C.The pressure
D.The volume occupied by the gas, which determines the number of microstates accessible to its molecules

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.

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Which process leaves the entropy of a parcel unchanged?

A.The evaporation of precipitation into the parcel as it descends through a layer of unsaturated air beneath
B.Reversible adiabatic ascent
C.Irreversible mixing with a neighbouring parcel of different potential temperature within the same layer
D.Isobaric heating

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.

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Which name is given to a surface of constant potential temperature?

A.An isopycnal surface
B.An isotherm, along which the actual temperature of the air remains the same at every point of the surface
C.An isentropic surface
D.An isobaric surface, on which the pressure rather than the potential temperature takes a fixed value throughout

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.

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Which motion do adiabatic parcels perform relative to those surfaces?

A.They cross the surface at a rate determined by the vertical velocity of the air at that particular level
B.They descend through it
C.They oscillate about the surface at the buoyancy frequency without ever remaining upon it for any period
D.They remain on the surface

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.

Discuss in Forum

Which slope do isentropic surfaces have in mid-latitudes?

A.They rise towards the pole
B.They rise towards the equator, since the warmer tropical air occupies a greater depth of the atmosphere there
C.They are horizontal
D.They slope steeply downward on the equatorward side and upward on the poleward side of the jet stream axis

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.

Discuss in Forum

Which vertical motion does poleward flow along such a surface produce?

A.Ascent during the summer and descent during the winter, according to the direction of the temperature gradient
B.Ascent
C.Descent, since the surfaces slope downward towards the pole where the air is colder and therefore denser
D.No vertical motion

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.

Discuss in Forum

Which chart displays the pressure on an isentropic surface?

A.A thickness chart
B.A cross section, which displays the vertical structure of the atmosphere along a chosen line through the domain
C.An isentropic analysis
D.A constant pressure chart, on which the geopotential height of a chosen pressure surface is contoured instead

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.

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Which function plays the role of the streamfunction on an isentropic surface?

A.The geopotential, whose gradient gives the geostrophic wind on a surface of constant pressure rather than entropy
B.The Exner function
C.The velocity potential, whose gradient gives the divergent component of the horizontal wind at that level
D.The Montgomery streamfunction

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.

Discuss in Forum

Which advantage does isentropic analysis have for trajectories?

A.Adiabatic trajectories remain on a single surface
B.The wind on an isentropic surface is exactly geostrophic, so no ageostrophic correction is ever required at all
C.It requires no wind data
D.The surfaces are horizontal, which reduces the trajectory calculation to a purely two dimensional problem

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.

Discuss in Forum

10.

Which process breaks the isentropic trajectory assumption?

A.The rotation of the Earth, which introduces a Coriolis deflection that a two dimensional method cannot handle
B.Diabatic heating such as latent heat release
C.Horizontal advection by the wind, which carries the parcel across the isentropic surface into the next one
D.Adiabatic ascent

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.

Discuss in Forum

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