The Relationship Between Pressure and Temperature: Answer to Question

1. Nothing
2. Parcel 1 is lighter than parcel 2
3. The two parcels have equal density
4. Parcel 2 is lighter than parcel 1

The correct answer is 2. The ideal gas law must be satisfied for both air parcels. Since the pressure is the same for each of them, the right-hand side of the equation must be the same for each of them, too. Since R* is constant, if one has a higher density, it must also have a lower temperature, and vice versa.

If, like me, you prefer to see how this works with real numbers, check out the numerical example.

Now, let's put what we know about pressure, density, and temperature together. Read through this slowly, because there's a lot going on and it's all important.

1. Air pressure is (approximately) equal to the weight (per unit area) of the column of air extending above that location to the top of the atmosphere.

2. The difference in air pressure between the top and bottom of an air column is (approximately) equal to the weight (per unit area) of the air column.

3. Denser air is heavier than lighter air.

THEREFORE, the more dense your air column, the bigger the change in air pressure over a given vertical distance.

In the above example, the pressure beneath the denser column is higher than the pressure beneath the lighter column, since the pressures at the top of the columns are equal.

Now, let's get back to the hydrostatic equation. Suppose you had two columns of air which featured exactly the same difference in air pressure between the top and bottom. What must be true?

1. They must be the same height.
2. They must have the same average air density.
3. They must be the same temperature.
4. If their heights are different, their densities must be different too.

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