Summary

• Temperature is the measure of hotness; heat is energy in transit due to a temperature difference.
• The Celsius, Fahrenheit, and Kelvin scales are related by: $T_C = T_K - 273.15$ and $\frac{T_C}{100} = \frac{T_F - 32}{180}$.
• Thermal expansion: linear $\Delta L = L_0 \alpha \Delta T$, areal $\Delta A = A_0 \beta \Delta T$ with $\beta = 2\alpha$, and volumetric $\Delta V = V_0 \gamma \Delta T$ with $\gamma = 3\alpha$.
• Specific heat capacity: $Q = m c \Delta T$; molar specific heat $C = M c$.
• Latent heat: $Q = m L$ (no temperature change during phase change).
• Calorimetry: heat lost by hot body = heat gained by cold body (in an isolated system).
• Heat transfer modes: conduction (Fourier's law $\frac{Q}{t} = k A \frac{T_1 - T_2}{d}$), convection (fluid motion), and radiation (Stefan-Boltzmann law $P = \sigma A e T^4$).
• Newton's law of cooling: rate of cooling $\propto$ temperature difference with surroundings; $\frac{dT}{dt} = -k (T - T_0)$.
• Thermal conductivity $k$: good conductors have high $k$; insulators have low $k$.
• Ideal gas equation: $PV = nRT$; absolute zero is $-273.15^\circ$C.

Quick Reference: Key Quantities, Symbols, Dimensions and Units