Thermodynamics and Kinetic Theory
What Thermodynamics and Kinetic Theory tests
This domain covers the laws of thermodynamics, heat and work, ideal gases, kinetic theory, entropy, and heat engines. Questions often require reading a PV diagram or choosing the correct sign for energy transfer.
Core rules
- First law, physics convention: ΔU = Q − W, where W is work done by the gas. For a cyclic process ΔU = 0, so Q = W.
- Ideal gas: PV = nRT. Average translational kinetic energy per molecule is (3/2)kBT; vrms = √(3kBT/m) = √(3RT/M).
- Isothermal work by an ideal gas: W = nRT ln(Vf/Vi). Adiabatic processes have Q = 0 and obey PV^γ = constant.
- Entropy change for reversible heat transfer: ΔS = Q/T. The second law says total entropy of an isolated system does not decrease.
- Maximum engine efficiency is the Carnot value 1 − TC/TH, with temperatures in kelvin.
Worked example
Two moles of an ideal gas expand isothermally at 300 K from 1.0 L to 2.0 L. Find the work done by the gas and the heat absorbed.
For an isothermal ideal-gas process, ΔU = 0, so Q = W. W = nRT ln(Vf/Vi) = (2)(8.314)(300) ln2 = 3.46 × 10^3 J. Thus the gas does about 3.5 kJ of work and absorbs about 3.5 kJ of heat.
Traps
Using Celsius in PV = nRT or Carnot efficiency; reversing the sign of work; assuming Q = 0 for any fast process without justification; treating vrms as proportional to T rather than √T; confusing internal energy with total heat.