First Law of Thermodynamics
High-Yield Summary
- First Law (Conservation of Energy): energy can't be created or destroyed, only converted; for a system, ΔE = q + w.
- Heat (q) and work (w) each have a sign convention based on the system's perspective; PV work (w = −PΔV) governs gas expansion/contraction.
- Heat transfers by conduction (molecular collisions), convection (fluid motion), or radiation (electromagnetic waves, no medium needed).
- Heat capacity links heat to temperature change: q = mcΔT. Water's high specific heat (4.18 J/g·K) makes it an effective coolant.
- Heating curves show temperature rising within a phase but plateauing during phase transitions (q = mL), since added energy breaks intermolecular forces rather than raising kinetic energy.
- Four thermodynamic processes — isothermal, adiabatic, isobaric, isochoric — each hold one quantity constant and produce a distinct P-V diagram shape.
First Law and Work
ΔE = q + w | w = F·d·cos θ | w = −PΔV
- q = Heat added to (+) or removed from (−) the system
- w = Work done on (+) or by (−) the system
- P, ΔV = Pressure and volume change, for PV work; 101.3 J = 1 L·atm
Heat Transfer Mechanisms
| Mechanism | How It Transfers Heat |
|---|---|
| Conduction | Molecule-to-molecule collisions; requires a medium (e.g., metal spoon in hot soup) |
| Convection | Physical motion of a fluid; requires a medium (e.g., water heating in a pot) |
| Radiation | Electromagnetic waves; no medium needed (e.g., sunlight through space) |
Heat Capacity and Phase Change
q = mcΔT | q = mL
- m = Mass
- c = Specific heat capacity (water = 4.18 J/g·K)
- ΔT = Temperature change
- L = Latent heat (heat of fusion or vaporization)
- q = mcΔT applies during a temperature change; q = mL applies during a phase change (temperature stays constant).
The Four Thermodynamic Processes
| Process | Held Constant / P-V Shape |
|---|---|
| Isothermal | Temperature constant; hyperbolic curve |
| Adiabatic | No heat exchange; steeper curve than isothermal |
| Isobaric | Pressure constant; horizontal line |
| Isochoric | Volume constant, no work done; vertical line |
Common MCAT Trap
- Temperature plateaus during melting/vaporization on a heating curve — this doesn't mean no energy is being absorbed; it means the energy is breaking intermolecular forces instead of raising kinetic energy (temperature).
- Watch sign convention on w: gas expanding does work on the surroundings, so w = −PΔV is negative for expansion (from the system's perspective) — don't flip the sign by accident.
Quick Recall
Why does temperature stay flat during a phase transition even as heat is added?
Which thermodynamic process does no work at all?
Which heat transfer mechanism can occur through a vacuum?