Understanding the Ideal Gas Law
Boyle's & Charles' Laws and Pressure, Volume & Temperature of Gasses
Oct 26, 2008
A hand pump inflating a bicycle tire will get hot. Why? It has to do with the behavior of gasses. When a gas is compressed into a smaller volume, its temperature and/or pressure increase. The reverse is also true. When allowed to expand rapidly, a gas's temperature decreases. One can freeze carbon dioxide by opening the valve of a compressed carbon dioxide gas cylinder and improvising a filter to catch the dry ice particles.
The mathematical relationships between the volume, pressure, and temperature of a gas are often taught and learned as separate laws: Boyle's law and Charles' law. However the ideal gas law encompasses both these laws in one mathematical formula.
Ideal Gas - Assumptions of the Ideal Gas Model
Ideal gasses do not really exist. It is an idealized concept that is approximated by real gasses. Physicists use such idealized concepts because they are mathematically simpler and are usually accurate enough.
For the ideal gas model, physicists assume that:
- The gas consists of atoms that are small hard spheres, and
- The atoms move about at random and interact only during occasional collisions.
Real gasses are very good approximations of ideal gasses if the density is not too high and the temperature is above the condensation temperature.
Ideal Gas Law - Pressure, Volume and Temperature of Gas (P, V, T)
The ideal gas law relates the pressure, volume, and temperature of a gas. For a given quantity of gas, the pressure, P, multiplied by the volume, V, divided by the temperature, T, remains a constant. In equation form:
PV/T = constant.
This form of the ideal gas law is useful for relative calculations. For example, a bicycle pump might decrease the volume of air to 1/4 its original volume during a pump stroke. The temperature, which must be measured on the Kelvin temperature scale, increases only a very small amount during one pump stroke. Hence during this pump stroke the pressure inside the pump increases to 4 times its original pressure and thereby pushes air into the tire being inflated.
Note that because the temperature in these calculations must be measured on the Kelvin temperature scale even an obvious temperature difference would be very small.
For absolute calculations, the ideal gas law can also be stated in the form:
PV = nRT
R = 8.31 J/moleK is the universal gas constant, and n represents the number of moles of gas present. An alternate form is:
PV = NkT
k = 1.38e(-23) J/K is the Boltzmann constant, and N represents the number of atoms or molecules of gas present.
Boyle's Law
Robert Boyle first discovered Boyle's law. It is a special case of the ideal gas law when the temperature does not change. If the temperature of a gas remains constant, then the pressure and volume are inversely related. As one increases, the other decreases.
In equation form, for the case of a constant temperature:
PV = constant
Charles' Law
Jacques Charles was a French hot air balloonist and scientist. He discovered Charles' law by studying the relationship between the volume and temperature of a gas at a constant atmospheric pressure. As the temperature of the gas in a balloon increased, its volume also increased. These increases inflated and lifted the balloon.
In equation form, for the case of a constant pressure:
V/T = constant
The ideal gas law is an elegant integration of gas laws that were discovered as separate laws for special cases. Physicists always look for such elegant ways to combine multiple laws into a single simple law.
Further Reading
Wilson,J.D, Buffa,A.J., & Lou,B. College Physics 6th ed., Pearson, 2007.
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