Temperature, Heat, and the First Law of Thermodynamics
This unit opens a genuinely different part of physics: instead of tracking individual particles or waves, thermodynamics tracks bulk, statistical properties of huge collections of them — temperature, heat, and internal energy. The first law of thermodynamics, ΔU=Q−W, is really just conservation of energy restated for thermal systems: whatever heat flows in, minus whatever work the system does on its surroundings, is exactly what's left over as a change in the system's internal energy.
What you'll learn
- Convert between Celsius, Fahrenheit, and Kelvin temperature scales.
- Calculate the heat required to change a substance's temperature, using specific heat.
- Calculate the heat required for a phase change, using latent heat.
- Solve calorimetry problems by setting heat lost equal to heat gained.
- Calculate linear thermal expansion of a solid.
- Apply the first law of thermodynamics, ΔU=Q−W, including calculating work done by a gas at constant pressure.
1. Temperature Scales and Heat
Temperature can be measured on several scales — Celsius, Fahrenheit, and Kelvin — but nearly every physics formula in this unit and the ones following it requires Kelvin, the absolute scale where 0 K genuinely means zero average molecular kinetic energy.
Heat is energy transferred due to a temperature difference, distinct from temperature itself. Raising a substance's temperature (without a phase change) requires Q=mcΔT, where specific heat c is an intrinsic material property — water's unusually high specific heat is why it heats up and cools down more slowly than most other common substances.
2. Phase Changes and Calorimetry
During a phase change (melting, freezing, boiling, condensing), temperature stays exactly constant even as heat continues to flow — all the energy goes into breaking or forming intermolecular bonds rather than changing kinetic energy: Q=mL, with no ΔT term at all.
Calorimetry problems (mixing substances at different temperatures) are solved by setting heat lost by the hotter substance equal to heat gained by the cooler one, since energy is conserved in an insulated system.
3. The First Law of Thermodynamics
The first law, ΔU=Q−W, restates energy conservation for thermodynamic systems: whatever heat flows into a system, minus whatever work the system does on its surroundings, equals the change in the system's internal energy. For a gas at constant pressure, work done by the gas is simply W=PΔV.
Sign conventions matter here: Q is positive when heat flows *into* the system, and W is positive when the system does work *on* its surroundings (as in expansion). Getting either sign backward flips the physical meaning of the result.
Key equations
- T(K) = T(°C) + 273.15 — Converting Celsius to Kelvin — the Kelvin scale is what almost every thermodynamics formula in this course actually requires.
- Q = mcΔT — Heat required to change a substance's temperature without a phase change.
- Q = mL — Heat required for a phase change (melting, freezing, boiling, condensing) at constant temperature — note there's no ΔT here, since temperature doesn't change during the phase change itself.
- ΔL = αL₀ΔT — Linear thermal expansion of a solid — how much a material's length changes with temperature.
- ΔU = Q − W — The first law of thermodynamics — energy conservation for a thermodynamic system. For a gas at constant pressure, W=PΔV.