Temperature is a measure of the average translational kinetic energy of particles in a system, and dictates the direction of spontaneous heat transfer: heat always flows from higher to lower temperature unless external work is applied. Three temperature scales exist, but only the absolute Kelvin scale is valid for thermodynamic calculations.
T(K) = T(^ ext{o}C) + 273.15
AP exams accept 273 instead of 273.15 with no point penalty.
Heat ($Q$) is energy transferred between systems due to a temperature difference, measured in Joules (J). Two key relationships describe heat transfer for temperature change and phase change.
Q = mc\Delta T
Q = mL
2. The Ideal Gas Law★★★☆☆⏱ 5 min
The ideal gas law describes the behavior of ideal gases, which follow four core assumptions: (1) gas molecules are point particles with negligible volume, (2) no intermolecular forces exist between molecules, (3) all collisions are perfectly elastic, (4) molecules move randomly. These assumptions hold for most real gases at low pressure and moderate temperature.
The ideal gas law combines Boyle's, Charles', and Avogadro's laws into two standard forms:
PV = nRT
Molar form: $P$ = pressure (Pascals), $V$ = volume ($m^3$), $n$ = moles of gas, $R = 8.31 J/(mol·K)$ (universal gas constant), $T$ = absolute temperature (K).
PV = Nk_B T
Molecular form: $N$ = number of molecules, $k_B = 1.38 \times 10^{-23} J/K$ (Boltzmann constant).
Kinetic molecular theory links temperature directly to average molecular kinetic energy:
\langle KE \rangle = \frac{3}{2}k_B T
3. Laws of Thermodynamics★★★☆☆⏱ 4 min
The first and second laws of thermodynamics define energy conservation and the direction of spontaneous thermal processes, which are core topics for AP Physics 2.
Sign conventions for AP Physics 2: $Q > 0$ if heat flows into the system, $Q < 0$ if heat flows out. $W > 0$ if the system does work on the surroundings (expansion), $W < 0$ if work is done on the system (compression).
4. PV Diagrams and Work Calculations★★★★☆⏱ 4 min
A pressure-volume (PV) diagram plots a gas' pressure against its volume as it undergoes a thermodynamic process. The work done by the gas between two volumes is equal to the area under the curve of the process.
W = \int_{V_1}^{V_2} P dV
For an isobaric (constant pressure) process, this simplifies to:
W = P\Delta V, \quad \Delta V = V_2 - V_1
**Isobaric**: Constant pressure, horizontal line on PV diagram, $W = P\Delta V$
**Isochoric (isovolumetric)**: Constant volume, vertical line on PV diagram, $\Delta V = 0$ so $W = 0$, all heat transfer changes internal energy
**Isothermal**: Constant temperature, hyperbolic curve ($PV = constant$), $\Delta U = 0$ for ideal gases so $Q = W$
**Adiabatic**: No heat transfer, $Q = 0$, steeper curve than isothermal, $\Delta U = -W$
Common Pitfalls
Why: You forget the conversion step, or assume temperature ratios work for Celsius even though temperature changes are the same on both scales
Why: Other sources or curricula use the opposite convention where $W$ is work done on the system, leading to sign errors
Why: You associate all heat transfer with temperature change, and forget phase changes occur at constant temperature
Why: You mix up the definition of work done on vs work done by the system
Why: Most exam problems use ideal gases, so you forget the assumptions of the ideal gas model