Work
High-Yield Summary
- Work is not energy — it's a measure of energy transfer via force applied over a displacement: W = Fd cos θ.
- Work is maximized when force and displacement align (θ = 0°), zero when perpendicular (θ = 90°), negative when opposed (θ = 180°).
- Gas work: W = PΔV, with a physics-vs-chemistry sign convention flip to watch for (w = −PΔV in chemistry).
- Power (P = W/Δt) measures how fast work is done.
- The work-energy theorem connects net work to kinetic energy change: Wnet = ΔK = Kf − Ki.
Work
W = Fd cos θ
- W = Work done
- F = Magnitude of the applied force
- d = Displacement of the object
- θ = Angle between the force and displacement direction
Angle Between Force and Displacement
| Angle (θ) | Effect on Work |
|---|---|
| 0° (force aligned with displacement) | Work maximized (cos θ = 1) |
| 90° (force perpendicular to displacement) | No work done (cos θ = 0) |
| 180° (force opposes displacement) | Work negative (cos θ = −1) |
Gas Work, Power, and the Work-Energy Theorem
W = PΔV | P = W/Δt | Wnet = ΔK = Kf − Ki
- P = Pressure (in gas work) or power (in P = W/Δt) — context-dependent
- ΔV = Change in gas volume
- Δt = Time over which work is performed
- Kf, Ki = Final and initial kinetic energy
- Physics convention: W = PΔV describes work done by the gas (expansion → positive W).
- Chemistry convention: w = −PΔV describes work done on the system (expansion → negative w). Same physics, opposite sign tracking.
Common MCAT Trap
- Watch which sign convention a passage is using for gas work — physics' W = PΔV (work by the gas) vs. chemistry's w = −PΔV (work on the system) describe the same process with opposite signs.
- No work is done when force is perpendicular to displacement, even if the force is large (e.g., carrying a bag while walking horizontally — gravity does no work on the bag).
Quick Recall
At what angle between force and displacement is work zero?
What does the work-energy theorem let you calculate without knowing the force or path?