Boyle’s law and Charles’ law are typically taught as an introduction to the equation of state (ideal gas law). These two laws are simplifications and special solutions of the equation of state in which the relationship between two variables can be studied in a lab setting. In Boyle’s law, the relationship between Pressure (P) and Volume (V) is analyzed. The form of Boyle’s law is: P*V = k, where k is a constant and the Temperature is constant. In this equation the mass is constant and the temperature is constant and the air is confined to a compressible and expandable volume. Since k is a constant, when either P or V change then the other variable has to change in a way such that the constant k stays fixed. This is accomplished by an indirect relationship which means when one goes up then the other has to go down. For example, if pressure increases then the volume will have to decrease in order for P*V to remain equal to a fixed constant. When air is compressed, the pressure increases. When air is expanded into a larger volume, then pressure decreases. In Charles’ law, the relationship between Temperature (T) and Volume (V) is analyzed. The form of Charles’ law is: V = k*T, where k is a constant and the pressure is constant. In this equation the mass is constant and the air is confined to a compressible and expandable volume. The temperature is also allowed in increase or decrease. Since k is a constant, when either V or T change then the other variable has to change in a way such that the constant k stays fixed. This is accomplished by a direct relationship which means when one goes up then the other has to also go up and when one goes down the other has to go down. For example, if Temperature increases then the Volume will have to increase in order for k to remain equal to a fixed constant. When air is compressed, the temperature decreases. When air is contracted into a smaller volume, then temperature decreases in order for the pressure to remain constant. If this seems counterintuitive to what happens in the atmosphere, it is. The difference between the lab tests and the real atmosphere is that in the real atmosphere, variables can not be held constant. Thus, the study of atmospheric thermodynamics will yield different results such as when studying adiabatic theory where temperature, pressure and volume can all three vary during a process. |