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Chapter 5: Q. 5.44 (page 177)

Suppose that an unsaturated air mass is rising and cooling at the dry adiabatic lapse rate found in problem 1.40. If the temperature at ground level is 25 C and the relative humidity there is 50%, at what altitude will this air mass become saturated so that condensation begins and a cloud forms (see Figure 5.18)? (Refer to the vapor pressure graph drawn in Problem 5.42)

Short Answer

Expert verified

The altitude at which air mass become saturated so that condensation begins and a cloud forms is 1.37 km

Step by step solution

01

Given information

(Refer table 5.11 and graph in problem 5.42)

At 25掳Cand50%relative humidity, the partial pressure of water is 0.016 bar.

The temperature at which this partial pressure is in equilibrium with vapour pressure is13.8掳C.

02

Estimating the height at which clouds will start forming.

From the dry adiabatic lapse rate for unsaturated air mass is

dTdZ=9.8掳C/km鈬�Z=1.14km

03

The height at which saturation begins.

The relation between pressure and height is

P(z)=Pe-z8.5

Substituting P=0.016 bar and z=1.14km

P(z) = 0.0014 bar

Using the graph in problem 5.42 we find this pressure is in equilibrium with vapour pressure at T=11.8掳C

For condensation to occur the temperature should reduce to 9.8掳C the air should rise a height.

04

determining the height

z=11.89.8(1.14)z=1.37鈮�1.40km

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Most popular questions from this chapter

In the previous section I derived the formula (鈭�F/鈭�V)T=-P. Explain why this formula makes intuitive sense, by discussing graphs of F vs. V with different slopes.

Repeat the preceding problem with T/TC=0.8

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CO2(g)+H2O(l)鉄�H2CO3(aq)

The carbonic acid can then dissociate into H* and bicarbonate ions,

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(The table at the back of this book gives thermodynamic data for both of these reactions.) Consider a body of otherwise pure water (or perhaps a raindrop) that is in equilibrium with the atmosphere near sea level, where the partial pressure of carbon dioxide is 3.4 x 10-4 bar (or 340 parts per million). Calculate the molality of carbonic acid and of bicarbonate ions in the water, and determine the pH of the solution. Note that even "natural" precipitation is somewhat acidic.

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