What is the Ideal Gas Law?
The ideal gas law was discovered in 1834 by physicist and engineer Benoît Paul Émile Clapeyron (1799 -1864). Clapeyron is one of the founding fathers of thermodynamics; he was the one who gave wide exposure to the little known work of Sadi Carnot, and he had a profound influence on Lord Kelvin and Clausius. The Clausius-Clapeyron equation, which describes the slope of phase boundary lines such as those between a liquid and gas, is named after him.
The ideal gas law is an equation of state that is very important and fundamental in thermodynamics. It is found by combining the laws of Boyle, Charles, and Gay-Lussac, into one elegant equation as follows below.
For a pressure P and volume V directly proportional to a temperature T we have:
1) PV ˜ T
2) PV ˜ mT,
where m is the mass of the gas.
All gases do not have the same mass so to simplify matters, we would like to have a constant that is the identical for all of them. For this reason, we convert m into a proportionality constant using a mole. The concept of a mole was previously discussed in Avogadro's Number.
Rewriting equation 2 in terms of moles, we have:
3) PV ˜ nT
4) PV = nRT.
R is a constant of proportionality called the universal gas constant, and in accordance with its name it is the same for all gases. Its value has been determined experimentally. In SI units of Joules and Kelvin, R is 8.315 J/(mol*K), while in BTU it is 1.99 calories/(mol*K). If we are interested in specifying volume in liters and pressure in atm, then R is 0.0821 (L*atm)/mol*K.
The ideal gas law applies for most gases in an equilibrium state where it is not too dense, and P is around atmospheric pressure. Real gases approximate these conditions enough such that the law is applicable in every day life.
In part two, we will learn how to use this law to find the mass of the total number of air particles inside your room.