Charles’ law states that for a gas at constant pressure, the volume divided by the temperature is a constant. This law is demonstrated in everyday life, such as in the expansion of dough and the filling of balloons. However, in the real world, particle size and interactive forces affect the mathematical deviation.
Charles’ law describes the relationship between volume and temperature of a gas. The law was attributed to the French scientist Jacques Charles by the chemist Joseph Louis Gay-Lussac, also French. Simply put, if the pressure remains constant, the volume of a gas divided by its temperature equals a constant. It can be deduced from the ideal gas equation, PV=nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is the Kelvin temperature. Rewriting the equation, V/T=(nR/P). Since P is constant, V/T=(constant).
Since the ratio equals a constant, V/T=K, a new temperature and volume for the same gas can be written V1/T1=K, leading to V/T= V1/T1. While this physical relationship is true for an ideal gas, the mathematical deviation occurs in the real world, as particle size and interactive forces have not been accounted for. However, if the temperature is high and the pressure is low, the particle volume becomes irrelevant. Similarly, because the pressure is low, the particles are far apart. This reduces the force interaction between the particles, which decreases with the square of the distance, making it insignificant.
While Charles’s law is simple, it explains many everyday observations. The yeast in the dough gives off tiny bubbles of carbon dioxide. Baking that dough expands the bubbles, resulting in lighter, fluffier pastries. Heating water in a boiler produces expansive steam, which is used to drive steam engines and keep classrooms warm. The gasoline automobile engine burns fuel, producing tremendous heat that expands the flue gases to drive the pistons that turn the crankshaft and power the vehicle.
Charles’s law is also demonstrated whenever a person opens a bottle or can of beer or soda. The containers of these drinks have pressurized carbon dioxide inside them. If a can or bottle of beverage is cold, opening the lid causes minimal gas expansion. With the same drink at a warm temperature, carbon dioxide will expand to a much greater extent. This can cause some contents to spill out of the can and onto the consumer.
Another simple application where Charles’ law can shed some light is filling a balloon. Volume (V), density (D) and mass (M) obey the relationship D=M/V. Rearranging gives V=M/D. Substituting this into Charles’ law V/T=(constant) gives M/DT=(constant). This modification of the law says that if a balloon is filled with gas and the temperature drops, the density will increase. If the balloon reaches a point where the outside air has a similar density to the inside air, the balloon will not rise any further.
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