Few students get really excited about thermodynamics, even though understanding thermodynamical concepts is essential for knowing the ways of the atmosphere.  Chapter 2 of Wallace and Hobbs covers many of the main points that you will study when you take Meteo 431, Atmospheric Thermodynamics next year.  It's treatment is sparse compared to Atmospheric Thermodynamics, by Bohren and Albrecht, as would be expected, but the major concepts are introduced.  It is our intent in this class to introduce you to the thermodynamical concepts and give you a chance to think about them before you go into much greater depth next year.

1.  What can we know about gases?

A gas is made up of individual molecules.  If you grab a handful of air, how many molecules do you capture?  We can determine a number and will probably be correct to within 10%.  However, you might say simply a bunch.  In fact, there would be so many molecules that many of their properties we can derive from them, not as individuals, but as a group.

This group of molecules has properties that can be related to one another with simple laws.  What is the simplest gas law that you know?  How about the equation of state, or the Ideal Gas Law:

where    p = pressure (force/unit area = kg / m s²);
            V = volume (m³);
            m = mass = n M, where n is the number of moles and M is the molecular weight in kg;
            R = gas constant (mass based) = 287 J /kg K (J = Nt m = kg m² / s²) for dry air = R*/Md
and      T = temperature (K)

where R* is the universal gas constant, 8.3143 J / mole K, or:

where r is the gas density, or:

where no = number of molecules and k = Boltzman constant = R*/Na, where Na is Avagadro's number.

All of these are equally valid.  The one we use depends on what we know and what we are trying to do.

Let's answer some questions.

1.  How many gas molecules can you hold in your hand?

2.  In a closed room, how does the pressure change if the temperature increases from 10 C to 30 C?  How much force does this put on the windows?

3.  What is the air density in State College today?  What is the air density where the airplane is flying overhead?  Why do we care how dense anything is anyway?

4. If we use the mass-based form of the ideal gas law, then we need a different gas constant for water vapor and for dry air.  Why?  What is the ratio of the gas constants?

5.  How much warmer does dry air have to be in order to have the same density as moist air?

This last question leads us to the concept of virtual temperature.

2.  Virtual temperature.

Virtual temperature is an attempt to equate the effects of gas composition on gas density to the effects of temperature.  In particular, it is a way to equate the density of moist air masses with that of dry airmasses by effectively normalizing out the fact that the moinst air contains significant amounts of water vapor.  The equation for virtual temperature is given by the expression:

As e/p increases, what happens to T_v for a given T?