Laws of perfect gases and their uses

1. Boyle's law states that the pressure and volume of a gas are inversely proportional, provided that the temperature and the number of moles of gas remain constant. This means that if the pressure of a gas is doubled, its volume will be halved. Conversely, if the volume of a gas is doubled, its pressure will be halved.
2. Charles's law states that the volume of a gas is directly proportional to its absolute temperature, provided that the pressure and the number of moles of gas remain constant. This means that if the temperature of a gas is doubled, its volume will also double. Conversely, if the volume of a gas is halved, its temperature will also be halved.
3. Gay-Lussac's law states that the pressure of a gas is directly proportional to its absolute temperature, provided that the volume and the number of moles of gas remain constant. This means that if the temperature of a gas is doubled, its pressure will also double. Conversely, if the pressure of a gas is halved, its temperature will also be halved.
4. Joule's law states that the internal energy of a gas is independent of its pressure and volume, provided that the temperature remains constant. This means that if the pressure or volume of a gas is changed, its internal energy will not change.
5. Regnault's law states that the specific heats of a gas do not change with the change of temperature and pressure. In other words, the specific heats of a gas are constant.
6. Avogadro's law states that equal volumes of different perfect gases at the same temperature and pressure contain an equal number of molecules. This means that the number of moles of gas in a volume is directly proportional to the temperature and pressure of the gas.

These gas laws are all based on the kinetic theory of gases, which states that gases are made up of tiny particles that are constantly moving and colliding with each other. The laws describe how the properties of gases change as the temperature, pressure, and volume of the gas change.

These gas laws are important in many fields, including physics, chemistry, and engineering. They are used to understand the behavior of gases in a variety of applications, such as the operation of engines, the design of pressure vessels, and the study of atmospheric phenomena.

Here are some examples of how these gas laws are used in everyday life:

• Boyle's law is used to explain how a bicycle pump works. When you pump air into a bicycle tire, you are increasing the pressure of the gas inside the tire. This causes the volume of the gas to decrease, which makes the tire harder.
• Charles's law is used to explain how a hot air balloon works. When the air inside a hot air balloon is heated, its temperature increases. This causes the volume of the gas to increase, which makes the balloon rise.
• Gay-Lussac's law is used to explain how a pressure cooker works. When you cook food in a pressure cooker, you increase the pressure of the gas inside the cooker. This causes the temperature of the food to increase, which makes it cook faster.
• Joule's law is used to explain why a car engine gets more efficient as it warms up. As the engine warms up, the temperature of the gas inside the engine increases. This causes the internal energy of the gas to increase, which makes the engine more efficient.
• Regnault's law is used to calibrate thermometers. The specific heats of a gas are known constants, so by measuring the change in the pressure of a gas as its temperature changes, you can determine the temperature of the gas.
• Avogadro's law is used to calculate the number of moles of a gas in a given volume. This is useful for calculating the amount of gas in a container or for determining the composition of a gas mixture.

Summary of topic:-

• Boyle's Law: States that at constant temperature the volume occupied by an ideal gas varies inversely with its absolute pressure. Mathematically

At constant temperature, p α 1/V or PV = constant

• Charles's law: States that at constant pressure the volume of the gas is directly proportional to the absolute temperature.

Mathematically,

At constant pressure, V α T or V/T= constant

 

• Characteristic gas equation pV= mRT

Where,

p = absolute pressure, N/m² or kN/m²

V volume of gas, m³

m = mass of gas, kg

T= absolute temperature, K.

R = characteristic gas constant, kJ/kgK.

• Universal gas constant : The product of molecular weight and characteristic gas constant is called universal gas constant.

Universal gas constant ,Ru = MR = 8.314kJ / l mole K.

• Joule's law: Internal energy of a gas is a function of temperature only and is independent of change in pressure and temperature. 
• Regnaults Law:- Specific heats of a perfect gas remains constant.

• Relation between specific heats and gas constant; Cp - Cv =R