Here begins the second apparently unrelated thread of our story. If we compress a gas, its temperature goes up. This occurs even if we don't allow any heat to enter the gas or leave it, say if we had gas inside an insulated piston that we compress or expand. The condition that we are describing, a closed system with no heat coming in or out, is called adiabatic. If gas is compressed adiabatically, it warms up. If you ever let the air out of a bicycle tire by holding the little valve open with your thumbnail, you may have noticed how cold your thumbnail got. The gas expanded as it flowed from the high-pressure tire into the lower-pressure atmosphere.

Figure 5.5 shows the temperature change that a parcel of dry surface air would experience if it were carried aloft adiabatically (an adiabatic trajectory or adiabat).

Compressible bricks Incompressible bricks

Fig. 5.4 A demonstration of why pressure changes rapidly at the bottom of the atmosphere and slowly at the top, because air in the atmosphere is compressible (left). For water, which is incompressible, pressure increases linearly with depth.

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Temperature (K)

Fig. 5.5 The temperature decrease with altitude in the atmosphere is called the lapse rate. If the atmosphere contained no water vapor, the lapse rate would follow the dry adiabat. As is, most of the atmosphere is closer to the moist adiabat, especially in the tropics where convection is most important.

150 200 250 300

Temperature (K)

Fig. 5.5 The temperature decrease with altitude in the atmosphere is called the lapse rate. If the atmosphere contained no water vapor, the lapse rate would follow the dry adiabat. As is, most of the atmosphere is closer to the moist adiabat, especially in the tropics where convection is most important.

We'll worry about water vapor in a moment, but for now we are looking at the line labeled dry adiabat (foreshadowing).

Why should the temperature go up in a gas as you compress it? It takes work to compress a gas. You have to squeeze our hypothetical insulated piston in order to compress it. Your muscles push against molecules bouncing against the walls of the cylinder. The work you put in is transformed into bouncing-around energy of the molecules of gas, its temperature. The situation is a little harder to envision for expansion because we tend to ignore the atmosphere around us and think of an empty room as empty space, but when the piston expands, it has to push back the atmosphere, in other words it must do work. The energy to do that work comes from the thermal energy of the molecules of the gas, so the gas cools as it expands.