Thermodynamics and Kinetic Theory
Thermodynamics and Kinetic Theory
This domain tests the first and second laws, ideal-gas behavior, kinetic theory, heat capacity, and thermodynamic processes. Questions often ask for an energy balance, a sign, or a comparison between two processes.
Core rules
- Use the physics sign convention ΔU = Q − W, where Q is heat added to the system and W is work done by the system. For a gas, W = PΔV at constant pressure; at constant volume W = 0.
- Internal energy of an ideal gas depends only on temperature. For a monatomic ideal gas, U = (3/2)nRT, C_V = (3/2)R, and C_P = C_V + R.
- Ideal gas law: PV = nRT, with T in kelvin. Kinetic theory gives average translational kinetic energy per molecule = (3/2)k_BT and v_rms = √(3RT/M).
- Isothermal means ΔT = 0; adiabatic means Q = 0; isobaric means constant pressure; isochoric means constant volume.
- The second law forbids a cyclic engine from converting all absorbed heat to work. Carnot efficiency is e = 1 − T_C/T_H.
Worked example
Two moles of monatomic ideal gas are heated at constant volume from 300 K to 400 K. Since volume is fixed, W = 0. Then Q = ΔU = nC_VΔT = (2)(3/2 × 8.31)(100) ≈ 2.5 × 10³ J. If the same gas were heated at constant pressure, it would absorb Q = nC_PΔT = (2)(5/2 × 8.31)(100) ≈ 4.2 × 10³ J, with part of the heat doing expansion work.
Traps
- Using Celsius temperatures in PV = nRT or in efficiency ratios.
- Reversing the sign of work: work done on the gas is negative in this convention.
- Treating heat and temperature as the same quantity.
- Using C_V for a constant-pressure process; C_P includes expansion work.