
Background on Ideal GasesRobert Boyle made the first quantitative measurements of gases in a systematic manner. Using a manometer, which measures differences in pressure, and a barometer, which measures the total pressure of the atmosphere, he developed what is now known as Boyle's law. This law states that at any constant temperature, the product of the pressure and the volume of any size sample of any gas is a constant, PV is constant when T is constant. Several years later, French chemist Jacques Charles formulated a general law known as Charles's law. This law states that at any constant pressure, the volume of any sample of any gas is directly proportional to the temperature, V/T is constant when P is constant. Discovered in 1802, the third gas law, GayLussac's law, states that the pressure of a fixed amount of gas at fixed volume is directly proportional to its temperature in kelvins. This law was named after the French chemist Joseph Louis GayLussac. It is expressed mathematically as P/T is constant when V is constant. Example of the three gas laws, here. Keep T const. for Boyle's law, P const. for Charles' law, and V const. for GayLussac's law. So we've heard of all these variables, but what exactly are they? The Ideal Gas Law
The three laws we just talked about describe three fundamental relationships between, P and T, V
and T, and V and P. Now, can combine the laws to make the combined gas law: P V = constant For atmospheric science, we don't want to think about a gas in terms of volume, it is hard to
calculate the volume of atmosphere over a given region. We want to think
about gases in terms of density, mass per unit volume. This is much easier to calculate. Using
density instead of volume gives us the common form of the Ideal Gas Law in atmospheric
science:
A. Medium T and P: The density of the air in the balloon (~ mass of molecules/volume) will also be medium. B. High T, Low P: The density of the air in the balloon (~ constant/larger volume) will be smaller. C. Low T, High P: The density of the air in the balloon (~ constant/smaller volume) will be larger. Now lets look at an application of the gas law. How do T, P, and &rho change when you change one variable at a time? Let's find out, click here for the applet.
This applet allows you to control the &rho (number of molecules and volume), P and T. Let's try a practice problemIf the temperature of an air parcel is 20.5 C, and its density is 0.690 kg/m^3, what is the
pressure of the air parcel, in mb?
&rho = 0.690 kg/m^3 R = 287 J/kg K So, p = 0.690 kg/m^3 * 252.5 K * 287 J/kg K = 50000 Pa In millibars, p ~ 50,000 Pa / 100(Pa/mb) = 500 mb Temperature and HeatHeat capacity is the amount of heat required per unit increase in temperature.
It is a measure of how well the substance stores heat, each substance has its own heat capacity
Specific Heat = (Heat capacity) / (mass), or c.
Substances with different specific heats require different amounts of energy. First Law of Thermodynamics
The first law of thermodynamics is the application of the conservation of energy principle to heat and
thermodynamic processes: Lets look at how the First Law of Thermodynamics is observed in our Ideal Gas Applet click here for the applet.
Based on the internal energy and work, is heat being added to the system or removed from the system? We will talk about heat and how it is transfered into or out of a system next week! The images and captions are derived from HyperPhysics, located at Georgia State University. 