Thermodynamics
Core concepts
Temperature and thermal equilibrium, heat capacity and calorimetry, latent heat of phase change, thermal expansion, and the three heat-transfer mechanisms (conduction, convection, radiation). The kinetic theory of gases connects temperature to average molecular kinetic energy. The laws of thermodynamics: energy conservation (first law, ΔU = Q − W), the direction of spontaneous processes and entropy (second law), and the unattainability of absolute zero (third law). Ideal gas law and simple thermodynamic processes (isothermal, adiabatic, isobaric, isochoric).
Traps to watch
- Heat vs. temperature: heat is energy in transit; temperature measures average molecular kinetic energy. Equal heat added does not mean equal temperature change.
- Latent heat: during a phase change temperature stays constant even though energy is added - a frequent graph-reading question.
- Sign of work: work done by the gas is positive in ΔU = Q − W; conventions differ, so match the equation given.
- Efficiency limits: no engine exceeds Carnot efficiency 1 − T_c/T_h, and temperatures must be in kelvin.
- Second law: entropy of an isolated system never decreases; local decreases require work input.
- Radiation needs no medium; conduction and convection do.
Rule of thumb
Convert all temperatures to kelvin before using the gas law, Carnot efficiency, or kinetic-theory relations. For calorimetry, set heat lost by the hot object equal to heat gained by the cold object plus any latent heat terms.
Worked example
How much heat raises 0.5 kg of water from 20 °C to 80 °C? (c = 4186 J/kg·°C) Q = mcΔT = 0.5 × 4186 × 60 ≈ 1.26 × 10⁵ J. If the water then boiled, add mL_v separately at constant temperature.
Modern Physics
Core concepts
Special relativity: the invariance of c, time dilation, length contraction, relativistic mass-energy (E = mc²). Quantum physics: photons and the photoelectric effect, the de Broglie wavelength, energy levels and atomic spectra, the Bohr model, and the uncertainty principle. Nuclear physics: alpha, beta, and gamma decay, half-life, and mass defect/binding energy. Also the wave-particle duality and the historical experiments (photoelectric effect, double slit) that established it.
Traps to watch
- Photoelectric effect: increasing intensity increases the number of electrons, not their maximum kinetic energy; only frequency (above the threshold) changes KE_max. This is the classic distractor.
- Photon energy: E = hf = hc/λ; shorter wavelength means higher energy.
- Half-life: after n half-lives, the fraction remaining is (½)ⁿ. It is never zero.
- Decay balancing: conserve mass number and atomic number across the equation; beta-minus increases Z by 1, alpha decreases A by 4 and Z by 2.
- Relativity: time dilation and length contraction apply to measurements by observers in relative motion; the proper time is measured in the rest frame.
- Bohr model limits: it works for hydrogen-like atoms only; multi-electron atoms need quantum mechanics.
Rule of thumb
For photoelectric problems, use K_max = hf − φ (work function). If hf is below φ, no emission occurs regardless of intensity - check the threshold before computing anything.
Worked example
Light of frequency 1.0 × 10¹⁵ Hz strikes a metal with work function 2.0 eV. K_max? hf = (6.63 × 10⁻³⁴)(1.0 × 10¹⁵) ≈ 6.63 × 10⁻¹⁹ J ≈ 4.14 eV. K_max ≈ 4.14 − 2.0 = 2.14 eV.
Scientific Inquiry
Core concepts
The scientific method as practiced: forming testable hypotheses, identifying variables (independent, dependent, controlled), designing controlled experiments, and distinguishing correlation from causation. Measurement: SI units, significant figures, precision vs. accuracy, random vs. systematic error, and uncertainty propagation. Data analysis: graphing, slope and intercept interpretation, linearization, and evaluating whether evidence supports a claim. Also the nature of science - peer review, reproducibility, and the tentative but self-correcting character of scientific knowledge.
Traps to watch
- Precision vs. accuracy: precision is repeatability; accuracy is closeness to the true value. A miscalibrated instrument is precise but inaccurate (systematic error).
- Independent vs. dependent: the independent variable is manipulated; the dependent variable is measured. Questions often reverse the wording.
- Control groups: a control isolates the effect of the treatment; without it, confounding variables weaken conclusions.
- Correlation is not causation - a lurking variable may explain both.
- Significant figures: multiplication and division keep the least number of sig figs; addition and subtraction keep the least decimal places.
- Graph slopes carry units and often represent a physical constant; always interpret slope and intercept, not just the shape.
Rule of thumb
When evaluating an experiment, ask three questions: Was one variable changed at a time? Was there a control or comparison? Could the measurement error explain the result? If any answer is no, the conclusion is not yet supported.
Worked example
A student measures g by timing a pendulum. Repeated trials give nearly identical periods (high precision) but the computed g is 5% low every time. This is systematic error - likely a mismeasured length or a calibration offset - not random scatter, so averaging more trials will not fix it; the apparatus must be corrected.