The Relationship Between Pressure and Temperature

Since pressure and density are so closely related, you might expect that temperature is closely related to pressure too. It is. The three quantities are tied together through the ideal gas law. You are probably familiar with the ideal gas law in the following form: pV = nRT (pressure times volume equals the number of molecules times the gas constant times temperature). Through a little bit of mathematical manipulation which I won't go into here, you can convert the terms involving volume and number of molecules into an expression involving density:

p = ρ(R*)T

Now R* is a constant. Imagine two air parcels at the same pressure (side by side). Suppose that parcel 1 is warmer than parcel 2.

What can you say about their densities?

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

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