Systems and Processes
High-Yield Summary
- Energy is the capacity to do work or produce heat; it's conserved (1st law) — never created/destroyed, only converted between potential and kinetic forms.
- System = reactants/products under focus; surroundings = everything else. Isolated (no energy/matter exchange), closed (energy only), open (both).
- Internal energy (E): ΔE(system) = −ΔE(surroundings). ΔE = q + w — heat (q) transfers via temperature difference, work (w) transfers via force through distance.
- State functions (T, P, V, E) depend only on current state; path functions (q, w) depend on the path taken.
- Four processes on a P-V diagram: isothermal (const T), adiabatic (no heat exchange), isobaric (const P), isochoric (const V). P-V work: w = −PΔV.
Key Terms
- System
- The part of the universe under focus (e.g., the reactants and products of a reaction).
- Surroundings
- Everything outside the system — the container, the room, etc.
- Isolated system
- Exchanges neither energy nor matter with surroundings (e.g., insulated bomb calorimeter).
- Closed system
- Exchanges energy but not matter (e.g., a steam radiator).
- Open system
- Exchanges both energy and matter (e.g., a pot of boiling water).
- Internal energy (E)
- The combined kinetic and potential energy of every particle in a system.
- State function
- A property depending only on the current state, not the path taken (T, P, V, E, H).
- Path function
- A property depending on the path taken between states (heat q, work w).
First Law of Thermodynamics
ΔE = q + w
- ΔE = change in internal energy of the system
- q = heat — positive when added to the system, negative when removed
- w = work — positive when done ON the system, negative when done BY the system
- Some sources write ΔE = q − w with an opposite sign convention for work — same physics, different convention.
- ΔE(system) = −ΔE(surroundings): total energy of the universe is conserved.
Pressure-Volume Work
w = −PΔV
- w = work done
- P = constant external pressure
- ΔV = change in volume
- Gas expands (ΔV > 0) → w negative: system does work on surroundings.
- Gas contracts (ΔV < 0) → w positive: surroundings do work on system.
- Conversion: 101.3 J = 1 L·atm.
The Four Thermodynamic Processes
| Process (constraint) | What happens / P-V diagram shape |
|---|---|
| Isothermal — constant T | Heat in = work out, T never changes. Hyperbolic curve (PV = nRT at const T). |
| Adiabatic — no heat exchange (q = 0) | ΔE comes entirely from work; T does change. Steeper curve than isothermal. |
| Isobaric — constant P | Volume changes, pressure fixed. Horizontal line. Heat changes both E and does work. |
| Isochoric — constant V | No work done (w = 0). Vertical line. Heat goes directly into internal energy, raising pressure. |
Must-Know Points
- 1 cal = 4.184 J; nutritional "Calorie" (capital C) = 1000 lowercase calories.
- Heat is NOT temperature: temperature measures average kinetic energy; heat measures the transfer of that energy between systems.
- Heat always flows from hotter to colder object.
- KE = ½mv² for a moving object; energy comes in potential (position/composition) and kinetic (motion) forms.
Common MCAT Trap
- Don't confuse state functions with path functions — T, P, V, E are state functions; q and w are path functions (depend on how you got there).
- Sign conventions for w vary by textbook (ΔE = q + w vs. q − w) — always check which convention a problem is using before assigning a sign.
- An isolated system exchanges neither energy nor matter — don't confuse with a closed system (energy only, no matter).
Quick Recall
A gas expands against constant external pressure. What's the sign of w?
Why is heat considered a path function rather than a state function?
Which of the four thermodynamic processes has w = 0, and why?