charles' law

Background:
Charles' Law:


Assuming that pressure remains constant, the volume and absolute temperature of a certain quantity of a gas are directly proportional.
Mathematically, this can be represented as:


Temperature = Constant x Volume
or
Volume = Constant x Temperature
or
Volume/Temperature = Constant
Substituting in variables, the formula is:


V/T=K
Because the formula is equal to a constant, it is possible to solve for a change in volume or temperature using a proportion:


V/T = V1/T1
Explanation and Discussion:

Charles' Law describes the direct relationship of temperature and volume of a gas. Assuming that pressure does not change, a doubling in absolute temperature of a gas causes a doubling of the volume of that gas. A drop of absolute temperature sees a proportional drop in volume. The volume of a gas increases by 1/273 of its volume at 0°C for every degree Celsius that the temperature rises.

To explain why this happens, let's explore temperature and volume in terms of gases. Temperature is an average of molecular motion. This means that, while all of the gas molecules are moving around their container in different directions at different speeds, they will have an average amount of energy that is the temperature of the gas. The volume of the gas is the size of its container because the molecules will move in a straight line until they impact something (another molecule or the container). However, to move as they do, the molecules require kinetic energy, which is measured by temperature.

So, the volume and temperature are very closely related. If the temperature was not sufficient, the molecules would not be able to overcome the weak forces of attraction among them and would not be able to fill the container.

Charles' Law must be used with the Kelvin temperature scale. This scale is an absolute temperature scale. At 0 K, there is no kinetic energy (Absolute Zero). According to Charles' Law, there would also be no volume at that temperature. This condition cannot be fulfilled because all known gases will liquify or solidify before reaching 0 K. The Kelvin temperature scale is Celcius minus 273.15 °. Therefore, zero Kelvin would be -273.15 ° and any Celcius temperature can be converted by to Kelvin by adding 273.15 (273 is often used).

Any unit of volume will work with Charles' Law, but the most common are liters (dm3) and milliliters (cm3).




The formula for the law is:


where:

V is the volume of the gas
T is the temperature of the gas (measured in Kelvin)
k is a constant.
In other more thermodynamics-based definitions, the relationship between the fixed mass of a gas at constant pressure is inversely proportional to the temperature applied to the system, which can be further used by stipulating a system where α represents cubic expansivity of a gas, with θ representing the temperature measured of the system in Kelvins:



V = Vo(1 + αθ)
To maintain the constant, k, during heating of a gas at fixed pressure, the volume must increase. Conversely, cooling the gas decreases the volume. The exact value of the constant need not be known to make use of the law in comparison between two volumes of gas at equal pressure:

.
Therefore, as temperature increases, the volume of the gas increases.