Gas Laws & Kinetic Theory

Gases are all around us -- the air we breathe, the LPG we cook with, the oxygen in hospitals. Unlike solids and liquids, gases can be easily compressed and they expand to fill any container. Understanding how pressure, volume, and temperature of gases are related is essential in physics and chemistry.

Boyle's Law (Constant Temperature)

At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.

P1 V1 = P2 V2 (at constant T)

Example: When you push a syringe plunger, the volume decreases and pressure increases.

Charles' Law (Constant Pressure)

At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature.

V1/T1 = V2/T2 (at constant P, T in Kelvin)

Example: A balloon expands when heated and shrinks when cooled.

Gay-Lussac's Law (Constant Volume)

At constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature.

P1/T1 = P2/T2 (at constant V, T in Kelvin)

Example: A pressure cooker -- as temperature increases, pressure increases inside the sealed vessel.

Ideal Gas Equation

Combining all three laws gives the ideal gas equation:

PV = nRT

where P is pressure (Pa), V is volume (m³), n is number of moles, R = 8.314 J/(mol K) is the universal gas constant, and T is temperature in Kelvin.

Worked Example

A gas occupies 500 cm³ at 27 C and 1 atm pressure. What volume will it occupy at 57 C and 2 atm?

Solution:

• Using P1 V1/T1 = P2 V2/T2
• T1 = 27 + 273 = 300 K, T2 = 57 + 273 = 330 K
• 1 x 500 / 300 = 2 x V2 / 330
• V2 = (500 x 330) / (300 x 2) = 165000 / 600
• V2 = 275 cm³

Kinetic Theory of Gases (KTG)

The kinetic theory explains gas behaviour using molecular motion:

• Gas consists of tiny molecules in random, continuous motion
• Collisions between molecules and with container walls are perfectly elastic
• The average kinetic energy of molecules is proportional to absolute temperature

Average KE per molecule = (3/2) kT where k = 1.38 x 10⁻²³ J/K (Boltzmann constant)

Nepal Connection

At high altitudes like Namche Bazaar (3,440 m), atmospheric pressure is lower. This is why water boils at a lower temperature in the mountains -- pressure cookers are essential for cooking dal bhat at altitude!

Key Takeaways

• Boyle's law: P inversely proportional to V (constant T)
• Charles' law: V proportional to T (constant P)
• The ideal gas equation PV = nRT combines all gas laws
• Temperature must always be in Kelvin for gas law calculations