Atlas MCAT Course
Equations & How to Use Them → Equations: Energy
Equations: Energy
Work, energy, springs, gases, and heat.
01The idea
Energy transfers, molecular motion, equilibrium, or spontaneity: these cues point to energy equations.
THREAD · Energy vs. rate
02Build the model
AWork: how forces transfer energy
Use when: a force causes displacement; you’re asked about energy gained or lost; direction of force matters.
Passage cues: “Pulled at an angle”, “Dragged across a surface”, “Applied force over distance”.
Don’t use it for: no displacement (no work!); purely perpendicular forces (e.g., centripetal).
BWork–energy theorem: connecting forces to speed changes
Use when: forces act over distance; speed changes; you want to avoid force-by-force analysis.
Passage cues: “Net work”, “Final speed”, “Slows down / speeds up”.
Don’t use it for: problems involving potential energy changes only; situations where momentum conservation applies better.
CConservation of mechanical energy: tracking energy without forces
Use when: only conservative forces act; heights, springs, or speeds change; the system is isolated.
Passage cues: “Frictionless”, “No energy lost”, “Closed system”.
Don’t use it for: friction, air resistance, or applied forces; non-isolated systems.
DHooke’s law and elastic potential energy: how springs store energy
Use when: springs stretch or compress; elastic restoring forces are present; spring compression relates to speed or height.
Passage cues: “Spring constant”, “Compressed by x”, “Restoring force”, “Maximum compression”.
Don’t use it for: plastic deformation; non-elastic materials.
EIdeal gas law: snapshot of molecular motion
Use when: gas state variables change; comparing pressure, volume, or temperature; closed gas systems.
Passage cues: “Sealed container”, “Temperature increases”, “Constant moles”.
Don’t use it for: phase changes; non-ideal, high-pressure systems (unless qualitative).
FCombined gas law: comparing two gas states
Use when: one sample of gas changes conditions; moles are constant; initial vs final states are compared.
Passage cues: “Before and after”, “Same amount of gas”.
GFirst law of thermodynamics: energy bookkeeping
Use when: heat transfer and work both occur; internal energy changes are discussed.
Passage cues: “System and surroundings”, “Heat absorbed”, “Work done by/on system”.
Don’t use it for: purely qualitative spontaneity questions.
HWork done by a gas: energy transferred during expansion or compression
Use when: gas expands or compresses; volume changes under pressure.
Passage cues: “Piston”, “Expansion”, “Compression”.
IHeat transfer: how temperature changes
Use when: temperature changes without phase change; heat capacity is relevant.
Passage cues: “Specific heat”, “Temperature increases”.
Don’t use it for: phase transitions (use latent heat conceptually).
JEntropy: dispersal of energy and matter
Use when: disorder or energy spreading is discussed; comparing microstates.
Passage cues: “Randomness”, “Microstates”, “Spontaneous mixing”.
Don’t use it for: mechanical-only problems.
03See the connections
The lesson names these links itself. Read the map left to right.
Mechanical
- Work, W_net = ΔKE
- Conservation of energy
- Springs
Gases
- PV = nRT
- Combined gas law
- W = PΔV
Heat
- ΔU = Q − W
- q = mcΔT
- Entropy
Next: flow equations.
04Reason with it
Four questions. Answer in your head first, then choose. You’ll see the reasoning either way.
Think first.
A box is pushed across a rough floor and its speed changes. Which equation avoids analyzing each force?
Think first.
A ball rolls down a frictionless ramp. Which equation fits best?
Think first.
A sealed gas sample is heated from 300 K to 600 K at constant volume. What happens to its pressure?
Think first.
A spring is compressed twice as far. How does its stored energy change?
05MCAT lens
MCAT shortcuts
No movement → no work
If friction appears → energy is not conserved
Springs store energy quadratically
Same gas, two states → combined gas law
Expansion = gas does work
More ways to arrange = higher entropy
06Common traps
Trap 1: Any force on a moving object does work
Misconception
Perpendicular forces do no work.
Correct model
Only the component along the motion counts.
Trap 2: Mechanical energy is always conserved
Misconception
Friction and applied forces change it.
Correct model
Use conservation only for isolated, frictionless systems.
Trap 3: Heat always raises temperature
Misconception
Not during a phase change.
Correct model
Use q = mcΔT only without a phase change.
07Dependency check
Can you reconstruct this concept without looking at the page? You should now be able to reason through:
When work is zero
Check against 02 · A.
When to use conservation vs work–energy
Check against 02 · B and C: friction decides.
How gases trade P, V, and T
Check against 02 · E and F.
How the first law tracks energy
Check against 02 · G and H.
If something feels unclear, the missing idea is usually thisEnergy methods track how much changes, not moment-by-moment how.
08Remember
REMEMBER · if you keep only a few things
- W = Fd cos θ; no displacement, no work.
- W_net = ΔKE.
- KE + PE constant only without friction.
- F = −kx; U = ½kx².
- PV = nRT; P₁V₁/T₁ = P₂V₂/T₂ (kelvin!).
- ΔU = Q − W; q = mcΔT; S = k_B ln W.
09Forward hook
Energy also drives fluids: pressure is energy per volume.
Which equation applies when something exerts pressure or flows through a tube?
That leads to the flow equations.
Next lessonEquations: Flow→