Adiabatic Processes and Lapse Rates Questions and Answers

Answer: A

The correct plot is P.

As the parcel rises its total pressure falls, and since no water is added or removed its mixing ratio stays fixed, so its vapour pressure falls in proportion to the total pressure: slowly, by roughly 10% per kilometre. The saturation vapour pressure depends only on temperature, and the parcel cools at the dry adiabatic rate of about 9.8 °C per km, so it falls much faster. With no nuclei for condensation, the two curves simply cross and the parcel becomes supersaturated above the crossing point. Plot P shows exactly this: a gently decreasing solid line crossed by a steeply decreasing dashed line.

In Q the vapour pressure falls much faster than the saturation value, in R the saturation vapour pressure increases with height, and in S the vapour pressure stays constant although the pressure decreases.

Answer: C

The process is Adiabatic heating or cooling.

In an adiabatic process no heat is exchanged with the surroundings. Rising air expands as pressure falls and cools; sinking air is compressed and warms. Dry air changes temperature at about 9.8°C per kilometre in this way, which is how rising air reaches its dew point and forms clouds.

Advection is the horizontal transport of heat or moisture by the wind. Deflation is wind erosion of loose material, and sublimation is the change of ice directly to vapour.

Answer: C

The dry adiabatic lapse rate is 9.8 K/km.

A rising parcel of unsaturated air expands and cools adiabatically. The rate is set by gravity and the specific heat of air at constant pressure:

\[ \begin{aligned} \Gamma_{d} &= \frac{g}{c_{p}} = \frac{9.81}{1004} \\ &\approx 9.8\ \mathrm{K/km} \end{aligned} \]

6.5 K/km is the average environmental lapse rate of the standard atmosphere. Around 5 to 6 K/km is typical of the saturated (moist) adiabatic lapse rate at low levels, which is smaller because condensation releases latent heat. 1.6 K/km is far too small.

Answer: B

The parcel is at -4 degree Celsius at 4 km.

Below the lifting condensation level the parcel is unsaturated and cools at the dry adiabatic lapse rate, about 10 degrees Celsius per km. Above the LCL it is saturated and cools at the given moist rate of 7 degrees per km.

\[ \begin{aligned} T_{2\,km} &= 30 - 10 \times 2 = 10\ ^{\circ}C \\ T_{4\,km} &= 10 - 7 \times 2 = -4\ ^{\circ}C \end{aligned} \]

Using the moist rate all the way up gives \(30 - 28 = 2\) degrees, which is not offered; using the dry rate all the way gives -10. None of -6, 0 or 6 degrees follows from applying the two rates to their own layers, and the warmer answers ignore the faster dry cooling below the cloud base.

Answer: C

The rate is about 10°C/1000 meters.

Unsaturated air that rises expands and cools adiabatically, and air that sinks is compressed and warms, at the dry adiabatic lapse rate:

\[ \begin{aligned} \Gamma_{d} &= \frac{g}{c_{p}} = \frac{9.81}{1004} \\ &\approx 9.8\ \text{K/km} \end{aligned} \]

That is close to 10°C per 1,000 m. Once air is saturated, latent heat released by condensation slows the cooling to the saturated (moist) adiabatic rate, about 5-6°C per 1,000 m. The other options, 20, 25 and 30°C per 1,000 m, are far steeper than any adiabatic rate.

Answer: A

The dry adiabatic lapse rate is gravity divided by the specific heat at constant pressure, which gives 9.81 divided by 1005 or about 9.8 kelvin per kilometre. It contains neither temperature nor pressure, which is why it is essentially constant throughout the troposphere and why the dry adiabat plots as a line of fixed slope. The environmental lapse rate is a property of the observed atmosphere rather than of a parcel, and confusing the two is the single commonest error in this topic.

Answer: B

Setting the heat exchange to zero in the first law and substituting hydrostatic balance gives the rate as \( g/c_p \) with no other dependence. Humidity alters the specific heat very slightly, giving 9.7 rather than 9.8 for very moist air, but the effect is negligible. The environment plays no part at all, since the parcel cools by its own expansion regardless of what surrounds it. The shared properties explain why these belong to one family, and the differences explain why more than one exists.

Answer: C

Latent heat released by condensation offsets part of the adiabatic cooling, so the saturated rate is smaller, ranging from about 4 kelvin per kilometre in warm moist air to nearly the dry value in very cold air. Condensation releases rather than removes heat, which is the point the second option gets wrong. The rate is not constant, which is why saturated adiabats are curved on a thermodynamic diagram. Working one numerical case through both cases side by side fixes the distinction better than any rule of thumb.

Answer: D

The rate depends on how much water is available to condense, and by Clausius-Clapeyron that is greatest at high temperature, so warm tropical air gives rates near 4 kelvin per kilometre. In very cold air there is almost no water and the rate approaches 9.8. This is why tropical soundings lie so much closer to the moist adiabat than polar ones do. Checking the units of each quantity catches a wrong formula before the arithmetic begins.

Answer: A

The environmental lapse rate is measured by a radiosonde and describes the actual atmosphere, averaging 6.5 kelvin per kilometre in the standard atmosphere but varying enormously in practice. The two adiabatic rates describe what a parcel would do, not what the environment does. Comparing the environmental rate with the two adiabatic rates is precisely how stability is assessed. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.