Chapter 12 — THE GOVERNING FUNDAMENTALS OF METEOROLOGY 



GAS LAWS 



The laws governing the behavior of gases 

 and mixtures of gases are given in the 

 following sections. 



Boyle's Law 



Boyle's law states that the volume of a 

 gas is inversely proportional to its pressure, 

 provided the temperature remains constant. 

 This means that if the volume is halved, the 

 pressure is doubled. 



The formula for Boyle's law is as follows: 



VP = V'P' 



For example, assume 20 cm* of gas has 

 a pressure of 1,000 mb. If the pressure is 

 increased to 1,015 mb and the temperature 

 remains constant, the new volume will be 

 19.71 cm 3 . Applying the formula, we find 



20 X 1,000 = V X 1,015 



v , _ 20,000 

 v ~ 1,015 



V = 19.71 cm 3 



Charles' Law 



In the section on the kinetic theory of gases, 

 it was explained that the temperature of a 

 gas is a measure of the average speed of the 

 molecules of the gas. It was also shown that 

 the pressure the gas exerts is a measure of 

 the number of times per second that the 

 molecules strike the walls of the container and 

 the speed at which they strike it. It then can 

 easily be seen that if the temperature of a 

 gas in a closed container is raised, the speed 

 of the molecules within the gas increases. This 

 causes the molecules to strike the sides of 

 the container more times per second and with 

 more force, since they are moving faster. Thus, 

 by increasing the temperature, the pressure is 

 increased. This is stated by Charles' law in 

 the following manner: If the volume of an 

 enclosed gas remains constant, the pressure 

 is directly proportional to the absolute tem- 

 perature. Therefore, if the absolute temperature 

 is doubled, the pressure is doubled; if the 

 absolute temperature is halved, the pressure 



is halved. The formulas for Charles' law are 

 p-pi = pi-p, where volume is constant, and 

 VT 1 = V'T where pressure in constant. 



For example, assume that 10 cm 3 of a 

 gas have a temperature of 200° absolute. If 

 the temperature is increased to 300° absolute, 

 the volume is 15 cm 3 . Applying the formula, 

 we find 



10 X 300 = V X 200 



v ^oir 



V = 15cm 3 



or applying T 1 and P', the same type relation- 

 ship can be computed. 



Universal Gas Law 



The universal gas law is a combination of 

 Boyle's law and Charles' law. It states that 

 the product of the initial pressure, initial 

 volume, and new temperature (absolute scale) 

 of an enclosed gas is equal to the product of 

 the new pressure, new volume, and initial 

 temperature. The formula is PVT* = P'V'T. 



For example assume the pressure of 

 500 cm 3 volume of gas is 600 mb and the 

 temperature is 30° C. (303° absolute). If the 

 temperature is increased to 45° C (318° 

 absolute) and the volume is decreased to 

 250 cm 3 , the pressure of the volume will be 

 1,259.4 mb. Applying the formula, we find 



600 X 500 X 318 = P' X 250 X 303 



pi _ 95,400,000 

 75,750 



P» = 1,259.4 mb 



Equation of State 



The Equation of State is a general formula 

 which gives the same information as Boyle's 

 law and Charles' law. It involves a gas constant, 

 which is a value assigned each gas. For instance, 

 the gas constant of air is 2,870 when the pressure 

 is expressed in millibars, and the density is 

 expressed in metric tons per cubic meter. 

 The constant may be expressed differently, 

 depending on the system of units used. The 



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