Table of Contents
- Combined Gas Law
- Boyle's Law
- Charles' law
- Gay Lussac's Law
- Application
- Reference
Combined Gas Law
Combined gas law states that the ratio of a gas's pressure-volume product to its absolute temperature is constant. It combines the relationships between temperature, pressure and volume of ideal gases as expressed in Charles's law, Boyle's law, and Gay-Lussac's law. Combined gas law is an amalgamation of these three laws, these laws each relate one thermodynamic variable to another mathematically while holding everything else constant. Let's go over the fundamentals of these three laws.
Boyle's Law
It states that under constant temperature, the pressure (p) of a given quantity of gas changes inversely with its volume (v). It describes how the pressure of a gas tends to decrease as the volume of the container increases. Mathematically it can be expressed as PV = k
For Example:
Assume you're a diver, and you're about to go on a dive with your lungs full of air. As you dive further into the water, the pressure in your lungs increases. When this happens, the air inside your lungs is compressed, resulting in a reduction in volume. As depicted in this figure, Boyle's law asserts that the higher the pressure (P), the lower the volume (V). k can be any constant number in this case.
Charles' law
It states that the volume of an ideal gas is directly proportional to the absolute temperature at constant pressure. When the pressure imposed on a sample of a dry gas is held constant, the Kelvin temperature and volume will be in direct proportion, according to the law. In simple terms, it describes how a gas expands as the temperature rises. A reduction in temperature, on the other hand, will result in a decrease in volume.
For Example:
Heating the air in the balloon increases the balloon’s volume. This decreases its density, so the balloon rises in the air. To come down, chilling the air (not-heating-it) allows the balloon to deflate. The gas becomes more dense and the balloon sinks. The shrinking balloon serves as a demonstration of Charles' law, which states that the higher the temperature (T), the higher the volume (V).
Gay - Lussac's law
Gay-Lussac’s law is states that the pressure exerted by a gas (of a given mass and kept at a constant volume) varies directly with the absolute temperature of the gas. In other words, the pressure exerted by a gas is proportional to the temperature of the gas when the mass is fixed and the volume is constant. The mathematical expression is as follows:
P ∝ T ; P/T = k
Where:
P is the pressure exerted by the gas
T is the absolute temperature of the gas
k is a constant.
For Example:
When a pressurized aerosol can (such as a deodorant can or a spray-paint can) is heated, the resulting increase in the pressure exerted by the gases on the container (owing to Gay-Lussac’s law) can result in an explosion. This is the reason why many pressurized containers have warning labels stating that the container must be kept away from fire and stored in a cool environment.
When you combine Boyle's law, Charles' law, and Gay-Lussac's Law you get the Combined Gas Law, which shows that:
- Pressure is directly proportional to temperature, or higher temperature equals higher pressure.
- Pressure is inversely proportional to volume, or higher volume equals lower pressure.
- Volume is directly proportional to temperature, or higher temperature equals higher volume.
Combined Gas Law Calculator
The equations in this calculator provide the solution to each of the for four components of this formula: (P) pressure, (V) volume, (T) temperature and even the constant (k), and the calculator automatically handles numerous unit conversions for pressure, volume and temperature. The combined gas law is mathematically expressed follows (click on a parameter):
The formula of the combined gas law is:
P • V / T = k
where:
- Pressure based on the Combine Gas Law: This computes pressure of the gas if you know volume, temperature and the combined gas constant for the specific gas.
- Volume based on the Combine Gas Law: This computes the volume of the gas if you know pressure, temperature and the combined gas constant for the specific gas.
- Temperature using the Combine Gas Law: This computes the temperature of the gas if you know pressure, volume and the combined gas constant for the specific gas.
- k gas constant using the Combine Gas Law: This computes the constant of proportionality of the gas if you know pressure, volume and the temperature for the specific gas.
How to effectively use the combined gas law
1) Write down all of the variable given by the problem
2) Identify what the unknown is
3) Solve for the unknown by plugging into the combined gas law calculator
Applications
The combined gas law has practical applications when dealing with gases at ordinary temperatures and pressures. Like other gas laws based on ideal behavior, it becomes less accurate at high temperatures and pressures. The law is used in thermodynamics and fluid mechanics. For example, it can be used to calculate pressure, volume, or temperature for the gas in clouds to forecast weather.
- Refrigeration
Another instance of the combined gas law applying to daily life is refrigeration. Refrigerators apply the combined gas law when they remove heat from their systems. The process of refrigeration starts when the compressed gas stored in refrigerator coils expands. This in turn lowers the temperature of the gas and transfers heat energy from the coil material to the gas. As gas is pumped through the coils, its pressure compresses the heat energy. This raises the temperature of the gas. Heat is released through the coils into the outside air, which in turn allows the refrigerator to stay cool. The cycle repeats when compressed gas is pumped through the system again.
2. Scuba Diving
One example of the combined gas law applies to scuba diving. In scuba divers, human lungs are the container that hold the gas. The pressure in water is greater than pressure in air, and water pressure increases with depth. With each additional foot that divers descend, water pressure rises. Therefore, divers must make adjustments to maintain the proper pressure balance between their lungs and the water. This change must also take place gradually to create an equilibrium. If a diver with full lungs ascends rapidly on a warm day, the volume of air in the lungs can expand quickly. Therefore, he or she must exhale quickly to allow gas in the lungs to escape.
References
Combined Gas Law Calculator | Calistry(2021). [online] Available at http://calistry.org/calculate/combinedGasLaw
http://calistry.org/calculate/combinedGasLaw
https://www.periodni.com/gas_laws_calculator.html.