Thermodynamics

1. Kinetic Theory of Gases

• Gases consist of a huge number of molecules in constant random motion.
• Temperature is a measure of the average kinetic energy of the molecules — higher temperature means faster average molecular motion.
• Pressure arises from molecules colliding with the container walls; more frequent/harder collisions mean higher pressure.

Common mistakes: thinking temperature measures the total energy of the gas (it measures the AVERAGE kinetic energy per molecule, independent of how much gas there is).

2. Ideal Gas Equation of State

• PV = nRT, where P = pressure, V = volume, n = number of moles, R = 8.31 J/(mol·K), T = temperature in Kelvin (always — never plug in Celsius directly).
• To convert: T(K) = T(°C) + 273.
• Isothermal process (constant T): P₁V₁ = P₂V₂.
• Isobaric process (constant P): V₁/T₁ = V₂/T₂.
• Isochoric process (constant V): P₁/T₁ = P₂/T₂.

Common mistakes: forgetting to convert Celsius to Kelvin before using PV=nRT (a very common and costly error); mixing up which quantity is held constant in isothermal/isobaric/isochoric problems.

3. First Law of Thermodynamics

• ΔU = Q − W, where ΔU is the change in internal energy, Q is heat added TO the system, and W is work done BY the system (on its surroundings, e.g. gas expanding).
• If work is done ON the gas instead (compression), W is negative in this convention, so ΔU = Q − (−|W|) = Q + |W|.
• This is simply a statement of conservation of energy applied to thermal systems.

Common mistakes: sign confusion — mixing up "work done BY the system" vs. "work done ON the system" flips the sign in the equation; forgetting that Q can be negative too (heat leaving the system).