Thermodynamics and Kinetic Theory
Thermodynamics and kinetic theory questions cover the ideal-gas law, internal energy, the first law, process graphs, heat engines and the molecular model of gases.
Core rules
- pV = nRT = NkT, with T always in kelvin. R = 8.31 J mol⁻¹ K⁻¹, k = 1.38×10⁻²³ J K⁻¹.
- Mean translational kinetic energy per molecule = (3/2)kT. For a monatomic ideal gas U = (3/2)nRT; for a rigid diatomic gas U = (5/2)nRT.
- First law: ΔU = Q − W, where W is work done by the gas. At constant pressure W = pΔV; at constant volume W = 0; isothermal means ΔU = 0; adiabatic means Q = 0.
- Molar heat capacities: C_p = C_v + R. For monatomic gases C_v = (3/2)R, C_p = (5/2)R.
- Heat-engine efficiency η = W/Q_in = 1 − Q_out/Q_in. Carnot limit η = 1 − T_c/T_h.
Worked example
2.0 mol of monatomic ideal gas is heated at constant volume from 300 K to 400 K. Since W = 0, Q = ΔU = (3/2)nRΔT = 1.5 × 2.0 × 8.31 × 100 = 2.49×10³ J. The pressure rises by the factor 400/300, but that is not needed for the energy calculation.
Traps
Substituting Celsius temperatures into pV = nRT; reversing the sign of work; using C_p for a constant-volume process; computing efficiency as Q_out/Q_in and exceeding 1; assuming an adiabatic process is isothermal.