First Law Applied to the Atmosphere Questions and Answers

Answer: C

Potential temperature is defined so that it does not change during adiabatic compression or expansion, which makes it the natural label for an air mass. The temperature itself falls on ascent, and the density falls too. The vapour pressure falls in proportion to the total pressure because it is the mixing ratio rather than the vapour pressure that is conserved. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: D

Bringing the parcel adiabatically to a standard reference pressure removes the effect of its current height, so that parcels at different levels can be compared directly. The reference of 1000 hectopascals is a convention chosen for arithmetic convenience. The other options define the dew point and the equivalent temperature, both of which answer different questions. Checking the units of each quantity catches a wrong formula before the arithmetic begins. The shared properties explain why these belong to one family, and the differences explain why more than one exists. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted. Checking the units of each quantity catches a wrong formula before the arithmetic begins. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: A

Integrating the first law for an adiabatic process gives \( \theta = T (p_0/p)^{R/c_p} \), with the exponent equal to 0.286 for dry air. Equivalently temperature equals potential temperature times the Exner function. The exponent follows directly from the integration and is not an empirical constant, which is worth noticing because it makes the formula easy to reconstruct. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: B

The exponent is \( R/c_p \), equal to 287 divided by 1005 or about 0.286. It is sometimes written as kappa. The ratio of specific heats gamma equals 1.4 and is related through \( R/c_p = (\gamma-1)/\gamma \), so the two are easily confused. Tracing each back to its definition prevents the confusion reliably.

Answer: C

Static stability requires potential temperature to increase with height, so that a parcel displaced upward finds itself cooler and denser than its surroundings and returns. Constant potential temperature indicates neutral stratification and a decrease indicates instability. This single criterion replaces the more cumbersome comparison of lapse rates and is the reason potential temperature is so central to the subject. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: D

A layer of constant potential temperature is one in which the actual temperature falls at exactly the dry adiabatic rate, so a displaced parcel finds itself with the same density as its surroundings. Well mixed convective boundary layers are close to this state. The second option describes a situation that cannot arise, since constant potential temperature and the dry adiabatic temperature profile are the same thing. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: A

Surface heating produces thermals that carry warm air upward and return cooler air downward, homogenising the potential temperature through the depth of the layer. The result is a nearly adiabatic temperature profile capped by a stable layer. Radiative cooling from cloud top can also drive mixing in stratocumulus, which makes that a genuine mechanism in a different setting. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: B

Vigorous mixing homogenises the conserved variables, so potential temperature and mixing ratio become uniform while the temperature falls at the dry adiabatic rate and the relative humidity rises. Recognising the signature on a sounding is a routine analytical skill. Constant temperature would indicate an isothermal layer, which is very stable rather than well mixed. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: C

For an ideal gas the specific entropy is the specific heat at constant pressure times the logarithm of the potential temperature, plus a constant. This is why an adiabatic reversible process, which conserves entropy, also conserves potential temperature. The identification makes isentropic and constant potential temperature surfaces the same thing. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: D

Because entropy is a function of potential temperature alone for an ideal gas, surfaces of constant potential temperature are surfaces of constant entropy. Adiabatic parcels remain on them, which is what makes isentropic analysis such a natural way to visualise three dimensional flow. Isobaric, isopycnal and isothermal surfaces are defined by other quantities entirely. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.