Thermodynamics and Kinetic Theory
Core concepts
Understand the ideal gas law (PV = nRT), the first law (ΔU = Q − W with work done by the gas), and the distinction between state functions (U, T, P, V) and path-dependent quantities (Q, W). Know the four basic processes: isothermal (ΔT = 0, ΔU = 0 for ideal gas), adiabatic (Q = 0), isobaric (W = PΔV), and isochoric (W = 0). For kinetic theory, connect average translational kinetic energy to temperature: KE_avg = (3/2)k_BT, and root-mean-square speed to molar mass. Recognize the second law in terms of entropy and the impossibility of a perfect heat engine; efficiency of a Carnot engine is 1 − T_c/T_h in kelvin.
Common traps
- Using Celsius instead of kelvin in gas-law and efficiency formulas.
- Sign errors in the first law: work done by the gas is positive when the gas expands.
- Assuming an isothermal process changes internal energy for an ideal gas (it does not).
- Confusing heat with temperature; a large heat transfer need not raise temperature much during a phase change.
Worked example
An ideal gas expands isothermally at 300 K, absorbing 500 J of heat. Since ΔU = 0, the work done by the gas equals Q = 500 J. If instead the expansion were adiabatic, Q = 0 and the gas would cool as it does work.
Rule of thumb
Convert every temperature to kelvin first; then classify the process to decide which of Q, W, or ΔU is zero.