ATOC 4720: classes 8&9 1. The gas laws 1. The gas laws 2. Virtual temperature 2. Virtual temperature

1. The gas laws Thermodynamics---important-- understanding atmospheric phenomena Thermodynamics---important-- understanding atmospheric phenomena Introduce fundamental ideas and relationships in thermodynamics & apply to atmospheric situation Introduce fundamental ideas and relationships in thermodynamics & apply to atmospheric situation

Equation of state: Ideal gas equation P, V, T equation of state Atmospheric gases---obey the ideal gas equation Application to dry and moist air

The ideal gas equation: P: pressure; V: volume, m: mass; T: temperature (Kelvin) R: gas constant for 1kg of a gas. Since

For a unit mass, m=1, Specific volume:

If the T of a fixed mass of gas is constant, the V of the gas is inversely Proportional to its pressure. Changes in the physical state of a body which occur at constant temperature Are termed: isothermal.

Charles’ two laws: [1] For a fixed mass of gas at constant pressure, the V of the gas is directly proportional to its absolute temperature. [1] For a fixed mass of gas at constant pressure, the V of the gas is directly proportional to its absolute temperature. [2] For a fixed mass of gas held within a fixed V, the pressure of the gas is proportional to its absolute temperature. [2] For a fixed mass of gas held within a fixed V, the pressure of the gas is proportional to its absolute temperature.

Definition: kilomole (kmol): a kilogram-molecular weight (or kmol) of a material is its molecular weight expressed in kilograms. For example: , One kmol of water is kg of water. The number of kilomoles n in mass m (kg) of material is:

According to this definition, the number of molecules in a kmol of any material is a universal constant--Avogadro’s number Hypothesis: gases containing the same number of molecules occupy the same V at the same T & P. Therefore, a kmole of any gas the value of R is the same and is referred to as the universal gas constant. For 1kmol,

We obtain :

As we know, The ideal gas equation for n kmol of any gas is:

The gas constant for one molecule of any gas is also a universal constant--Boltzmann’s Constant k. For unit mass dry air: Where is the gas constant for 1kg of dry air.

Because: How much is “n” for 1km of air? We know:

28.97

Apply to individual gas Water vapor:

Dalton’s law The total P of a mixture of gases which do not interact chemically is equal to the sum of the partial pressures of gases.

2. Virtual temperature Moist air: V, T, total P, which contains: Md and Mv. Partial densities.

Dalton’s law: Combining the above equations:

Or, Where, Moist air : Where, Virtual T