SCIENCE · INVESTIGATE AND EXPLAIN

Distinguish four thermal-process constraints

Words such as isothermal and adiabatic describe different constraints. Isothermal means constant temperature; adiabatic means no heat transfer. One does not imply the other. Isochoric means constant volume, and isobaric means constant pressure. Always identify which condition is being imposed before selecting an energy relation.

Learning outcome: Capture constant-pressure and constant-volume cases at ratio 1.5, then constant-temperature and adiabatic cases at the same volume ratio. Reconstruct every ledger using ΔU=Q+Won. Do not compare the ratio labels as though all four control temperature.

Starting recap

Use absolute temperature, signed energy changes, algebraic ratios and graph areas. State the system boundary and distinguish heat transfer from temperature.

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Try

For nR=1 J/K initially at 300 K, a constant-pressure temperature increase to 450 K gives ΔU=225 J, Wby=150 J and Q=375 J. At constant volume the same temperature increase needs Q=225 J because volume work is zero.

Open the experiment

Predict

For a volume expansion, compare the signs of ΔU and Q in isothermal and adiabatic cases.

Your prediction and reason

Experiment

Capture constant-pressure and constant-volume cases at ratio 1.5, then constant-temperature and adiabatic cases at the same volume ratio. Reconstruct every ledger using ΔU=Q+Won. Do not compare the ratio labels as though all four control temperature.

Separate isochoric, isobaric, isothermal and adiabatic constraints

Worked teaching model · synthetic values · Monatomic ideal gas, nR=1 J/K, initial T=300 K,V=3 L,P=100 kPa. Processes are quasistatic; adiabatic path is reversible with γ=5/3. Logarithmic/power-law path calculations are supplied numerical enrichment, not required calculus. Use W_on=−W_by.

Process: 0=constant V, 1=constant P, 2=constant T, 3=adiabatic: 1 process Final/initial temperature ratio for 0; volume ratio otherwise: 1.5 ratio

Reset keeps your prediction, captures and practice history.

Axes rescale with settings; compare numerical values, not screen angles or apparent lengths. Solid/points show the selected model relationship or observations; the dashed comparison is explained below.

Calculated evidence ledger — synthetic teaching model
Quantity	Value	Unit
Final temperature	450	K
Final volume	4.5	L
Final pressure	100	kPa
Internal energy change	225	J
Work on gas	-150	J
Heat into gas	375	J

Accessible plot coordinates

Primary plotted points
volume (L)	pressure (kPa)
3	100
3.075	100
3.15	100
3.225	100
3.3	100
3.375	100
3.45	100
3.525	100
3.6	100
3.675	100
3.75	100
3.825	100
3.9	100
3.975	100
4.05	100
4.125	100
4.2	100
4.275	100
4.35	100
4.425	100
4.5	100

At constant pressure, some input heat leaves as expansion work.

All values use nR=1 J/K and U=(3/2)nRT. The supplied isothermal logarithm and reversible adiabatic power law generate numerical comparisons; AP reasoning does not require deriving those functions. A ratio below 1 reverses the thermal/volume change; identify the controlled quantity before comparing.

At constant pressure, some input heat leaves as expansion work.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Establish the model and evidence

For the monatomic ideal gas here, U=3nRT/2. An isothermal expansion therefore has no internal-energy change even though work is delivered and heat enters. An adiabatic expansion instead supplies its work by reducing internal energy, so the gas cools. At constant volume there is no PV work, while at constant pressure some supplied heat accompanies expansion.

The model generates complete quasistatic paths and supplies their numerical work. The isothermal logarithm and reversible-adiabatic power law are computational enrichment: you need not derive these functions to explain the AP-level energy comparisons. For the adiabatic curve, reversible and monatomic are additional assumptions, not synonyms for adiabatic.

The ratio control has a different declared meaning for the constant-volume case: it changes temperature rather than volume. A ratio below one reverses the change. Read the setting label and final-state table before comparing. A real process may exchange heat and work simultaneously without fitting any of the four idealized constraints exactly.

For a general material, internal energy includes microscopic kinetic energy and interaction/configuration potential energy. The special monatomic ideal-gas relation used here omits intermolecular potential energy and additional internal degrees of freedom. It must not be extended to claim that every substance at a fixed temperature has unchanged internal energy during a phase change.

Worked evidence

Predict and investigate

For a volume expansion, compare the signs of ΔU and Q in isothermal and adiabatic cases.

Transfer to changed conditions

A closed gas receives 80 J as heat while 120 J of work is done on it. What is ΔU? Is its process adiabatic?

Compare the worked transfer

ΔU=80+120=200 J. It is not adiabatic because Q is nonzero; temperature inference additionally needs an internal-energy model.

Explain the boundary

Explain a counterexample to “no heat transfer means no temperature change.” Identify the extra assumption behind the displayed adiabatic path shape.

Sources and authorship

Physical relationship reference. Current AP Physics 2 framework, checked 30 October 2026. The numerical cases, text and computed representations are original. All browser evidence is synthetic or calculated, not a record of completed practical work. No hazardous apparatus is required.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Explain a counterexample to “no heat transfer means no temperature change.” Identify the extra assumption behind the displayed adiabatic path shape.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Use PV area without confusing path and state Next: Distinguish uncertainty from omitted thermal pathways

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