Thermodynamics and Kinetic Theory
Thermodynamics and Kinetic Theory: what is tested
This domain tests temperature and heat, ideal gases, the kinetic model, and the first and second laws. Expect questions that combine a gas law with an energy balance, or that ask you to interpret a pressure–volume process.
Core rules
- Convert to kelvin: T(K) = T(°C) + 273.15. Gas-law calculations require absolute temperature.
- Heat transfer without a phase change is Q = mcΔT; during a phase change Q = mL. Heat and temperature are different quantities.
- Ideal gas: pV = nRT = NkT. Average translational kinetic energy per molecule is (3/2)kT; internal energy of a monatomic ideal gas is (3/2)nRT.
- First law: ΔU = Q − W, where W is work done by the gas. Work is the area under a p–V graph; at constant pressure W = pΔV.
- Isothermal: ΔU = 0 for an ideal gas. Adiabatic: Q = 0, so ΔU = −W. Isochoric: W = 0. Isobaric: W = pΔV.
- Second law: entropy of an isolated system does not decrease. Heat engines have efficiency η = W/Q_H, and the Carnot limit is η = 1 − T_C/T_H.
Worked example
A gas absorbs 500 J of heat and does 200 J of work on its surroundings. Using ΔU = Q − W gives ΔU = 500 − 200 = 300 J. The internal energy rises because the heat absorbed exceeds the energy leaving as work. If the same gas then expands isothermally, its internal energy stays constant, so the heat absorbed equals the work done during that process.
Traps that cost marks
Using degrees Celsius in pV = nRT is a common error. Watch the sign of work: work done by the gas is positive in ΔU = Q − W. Do not assume ΔU = 0 for every expansion; it is zero only for an isothermal process involving an ideal gas. In an adiabatic process Q = 0, not ΔU = 0. Efficiency cannot exceed the Carnot value, and no real engine reaches it. Internal energy of an ideal gas depends only on temperature, not pressure or volume separately.