1. Thermodynamics Gas Laws

2. Take the pressure down – Yo!
Boyle's Law
Take the pressure down – Yo!
Boyle's law (sometimes referred to as the Boyle-Mariotte law) is one of the gas laws and basis of derivation for the ideal gas law, which describes the relationship between the product pressure and volume within a closed system as constant when temperature and moles remain at a fixed measure; both entities remain inversely proportional.
The law was named after chemist and physicist, Robert Boyle who published the original law in The law itself can be defined succinctly as follows:
“For a fixed amount of gas kept at a fixed temperature, P and V are inversely proportional (while one increases, the other decreases).

3. “For a fixed amount of gas kept at a fixed temperature, P and V are inversely proportional (while one increases, the other decreases).

4. Equation The mathematical equation for Boyle's law is: where:
PV = k (constant)
where:
P denotes the pressure of the system.
V is the volume of the gas.
k is a constant value representative of the pressure and volume of the system.

5. So long as temperature remains constant at the same value the same amount of energy given to the system persists throughout its operation and therefore, theoretically, the value of k will remain constant.
Forcing the volume V of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure P must decrease proportionally.
Conversely, reducing the volume of the gas increases the pressure.

6. Boyle's law is commonly used to predict the result of introducing a change, in volume and pressure only, to the initial state of a fixed quantity of gas.
The "before" and "after" volumes and pressures of the fixed amount of gas, where the "before" and "after" temperatures are the same (heating or cooling will be required to meet this condition), are related by the equation:
P1V1 = P2V2

7. Charles’s Law
Hot Stuff!
In thermodynamics and physical chemistry, Charles's law is a gas law and specific instance of the ideal gas law, which states that:
At constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in Kelvin) increases or decreases.

8. Equation The formula for the law is: where: V = k T
V is the volume of the gas
T is the temperature of the gas (measured in Kelvin)
k is a constant.

9. 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 of a gas, with θ representing the temperature measured of the system in Kelvins:
V α T

10. 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.
Theoretically as a gas reaches absolute zero the volume will also reach a point of zero.

11. Gasses make me so happy! He He
Gay-Lussac's Law
Gasses make me so happy! He He
Pressure-temperature law
The other law, discovered in 1802, states that:
The pressure of a fixed amount of gas at a fixed volume is directly proportional to its temperature in Kelvins.
Simply put, if a gas's temperature increases then so does its pressure, if the mass and volume of the gas are held constant.

12. Equation The law is expressed mathematically as: or where:
P is the pressure of the gas.
T is the temperature of the gas (measured in Kelvins).
k is a constant.
This law holds true because temperature is a measure of the average kinetic energy of a substance; as the kinetic energy of a gas increases, its particles collide with the container walls more rapidly, thereby exerting increased pressure.

13. For comparing the same substance under two different sets of conditions, the law can be written as:
Charles's Law was also known as the Law of Charles and Gay-Lussac, because Gay-Lussac published it in 1802 using much of Charles' unpublished data from 1787.
However, in recent years the term has fallen out of favour since Gay-Lussac has the second but related law presented here and attributed to him.

14. Ideal Gas Law
The ideal gas law is the equation of state of a hypothetical ideal gas, first stated by Benoît Paul Émile Clapeyron in 1834.
The state of an amount of gas is determined by its pressure, volume, and temperature according to the equation:
where
P is the absolute pressure of the gas,
V is the volume of the gas,
n is the number of moles of gas,
R is the universal gas constant, = J·mol−1·K−1
T is the absolute temperature.