SCIENCE · INVESTIGATE AND EXPLAIN

Use PV area without confusing path and state

Pressure and volume locate a state on a PV diagram. A sequence of states specifies a path, and the path matters for work. For a quasistatic expansion, the moving boundary transfers energy to the surroundings. The work done by the gas is positive; the AP convention for work done on the gas is negative.

Learning outcome: At final volume 4 L, capture all three paths. Calculate signed work-on and heat before reading their ledgers. Repeat at 5 L and explain why the difference between the low/high paths grows.

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

From (2 L, 100 kPa) to (4 L, 200 kPa), low-pressure-first expansion gives Wby=200 J, high-pressure expansion gives 400 J, and the straight path gives 300 J. All have ΔU=1.5(800−200)=900 J, so Q is 1100, 1300 or 1200 J.

Open the experiment

Predict

Predict whether changing the path can change final internal energy when initial and final states remain fixed.

Your prediction and reason

Experiment

At final volume 4 L, capture all three paths. Calculate signed work-on and heat before reading their ledgers. Repeat at 5 L and explain why the difference between the low/high paths grows.

Compare work for shared end states

Worked teaching model · synthetic values · Quasistatic monatomic ideal gas with nR=1 J/K. Start (2 L, 100 kPa); finish (selected L, 200 kPa). Gas and external pressures match in the reversible-limit work calculation. 1 kPa L=1 J. This is a virtual path, not apparatus instructions.

Path: 0=expand then heat, 1=heat then expand, 2=straight PV path: 0 path Final volume: 4 L

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Calculated evidence ledger — synthetic teaching model
Quantity	Value	Unit
Initial temperature	200	K
Final temperature	800	K
Work by gas	200	J
Work on gas	-200	J
Internal energy change	900	J
Heat into gas	1100	J

Accessible plot coordinates

Primary plotted points
volume (L)	pressure (kPa)
2	100
4	100
4	200

Shared end states fix ΔU but do not fix work or heat.

The area under each quasistatic PV path gives W_by. Use the AP work-on convention ΔU=Q+W_on, with W_on=−W_by. Vertical segments do no volume work. Pressures are absolute;1 kPa L equals 1 J.

Shared end states fix ΔU but do not fix work or heat.

The area under each quasistatic PV path gives W_by. Use the AP work-on convention ΔU=Q+W_on, with W_on=−W_by. Vertical segments do no volume work. Pressures are absolute;1 kPa L equals 1 J.

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 a constant-pressure segment, Wby=PΔV. A vertical segment changes pressure at constant volume and contributes no volume work. A straight sloping segment uses the average pressure times the volume change. These geometric areas are algebraic tools, not a requirement to perform calculus. The unit identity 1 kPa L = 1 J makes the ledger particularly transparent.

The model sends the same monatomic ideal gas between the same initial and final states using three paths. Because nR is fixed at 1 J/K, T numerically equals PV when pressure is in kPa and volume in litres. Internal energy depends only on temperature: U=3nRT/2. Thus all three paths have the same ΔU but can require different heat inputs.

Write the first law with named signs: ΔU=Q+Won, where Q is positive into the gas and Won=−Wby. Do not mix this with a textbook equation using Wby without changing the sign. The pressure-area interpretation also assumes the path represents a sufficiently slow boundary process; an arbitrary nonequilibrium gas pressure is not automatically the external pressure that determines work.

Worked evidence

Predict and investigate

Predict whether changing the path can change final internal energy when initial and final states remain fixed.

At final volume 4 L, capture all three paths. Calculate signed work-on and heat before reading their ledgers. Repeat at 5 L and explain why the difference between the low/high paths grows.

Transfer to changed conditions

A gas expands from 1 L to 3 L at 150 kPa and its internal energy increases by 200 J. Find Won and Q.

Compare the worked transfer

Wby=150×2=300 J, Won=−300 J and Q=ΔU−Won=500 J.

Explain the boundary

Explain what is a state function and which two quantities depend on path. Translate the first law between work-on and work-by conventions explicitly.

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 what is a state function and which two quantities depend on path. Translate the first law between work-on and work-by conventions explicitly.

Your explanation and limitations

Continue

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

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Previous: Choose a system boundary for thermal equilibration Next: Distinguish four thermal-process constraints

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