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. Therefore, 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 often per second and with more force because they are moving faster. Thus, by increas-ing the temperature, the pressure is increased.
Charles law states if the volume of anenclosed gas remains constant, the pressure is directly proportional to the absolute temperature. Therefore, if the absolute temperature is doubled, the pressure is doubled; if the absolute temperature is halved, the pressure is halved. Experiments show that the volume increases by 1/273 for a 1°C rise in temperature. (Remember, 0°C is equal to 273°K.) An example of Charles law is a bottle of soda or beer. When the soda or beer is cold, very little pressure is released when the bottle is opened. When a warm soda or beer is opened, it often results in enough pressure buildup in the bottle to squirt soda or beer out of the top. Sometimes, warm soda or beer ex-plodes spontaneously when exposed to too much direct heat such as sunlight.
The formulas for Charles law are as follows:
VTī = Vī T, where pressure is assumed to be constant, and
PTī = Pī T, where volume is constant
V= initial volume
T= initial temperature (absolute)
Vī = new volume
Tī = new temperature (absolute)
For example, assume that 10 cm3 of a gas has a temperature of 200° absolute. If the temperature is increased to 300° absolute, what will be the new volume? Applying the formula, we have
V = 10 cm3
T = 200°K
Vī = Unknown in cm3
Tī = 300°K
The same type relationship can be computed
The same type relationship can be computedby applying Tī (new temperature) and Pī (new pressure) using the formula PTī = Pī T where the volume is assumed to remain constant.