AP Physics 2 · Exam guide
AP Physics 2 Thermodynamics FRQ Explained: PV Diagrams and the First Law
Thermodynamics is one of the three largest units in AP Physics 2, and PV diagrams are a favorite free-response setting. A question gives a process on a graph of pressure against volume and asks about work, heat and internal energy. The numbers below are made up for practice.
The relationships to know
| Quantity | Relationship |
|---|---|
| First law | \(\Delta U = Q + W\), where W is the work done on the system and Q is the energy added by heating. |
| Work at constant pressure | \(W = -P\Delta V\). The gas does work when it expands (W is negative) and has work done on it when it is compressed (W is positive). |
| Work on a PV diagram | The area under the curve, with a sign set by the direction of the volume change. |
| Internal energy of an ideal gas | Depends on temperature. If the temperature does not change, \(\Delta U = 0\). |
A worked example (made-up numbers)
A gas expands at a constant pressure of \(2.0 \times 10^5\) Pa from \(1.0 \times 10^{-3}\) m\(^3\) to \(3.0 \times 10^{-3}\) m\(^3\) while absorbing 1000 J of heat. Find the work done on the gas and the change in internal energy.
- Change in volume: \(\Delta V = 3.0 \times 10^{-3} - 1.0 \times 10^{-3}\), which is \(2.0 \times 10^{-3}\) m\(^3\).
- Work on the gas: \(W = -P\Delta V\), so \(W = -(2.0 \times 10^5)(2.0 \times 10^{-3})\), which is \(-400\) J.
- First law: \(\Delta U = Q + W = 1000 + (-400) = 600\) J.
A follow-up asks whether the temperature of the gas increased, decreased or stayed the same.
It ignores the work the gas did, which carried some of the energy away.
It uses the calculated value of the change in internal energy and the connection to temperature.
A three-step method
- Decide the sign of \(\Delta U\) from whether the temperature rises, falls or stays the same.
- Find W from the volume change or the area under the curve, with the right sign.
- Solve the first law for whatever is unknown, and say what the sign means.
Common mistakes
- Mixing up the sign of W. Expansion means the gas does work, so W on the gas is negative.
- Using the first law with \(Q\) and \(W\) in different sign conventions in the same problem.
- Forgetting that \(\Delta U = 0\) when the temperature stays the same.
- Reporting an area on the graph without units of joules.
Frequently asked questions
Which sign convention does this course use for work?
W is the work done on the system, so the first law is change in internal energy equals Q plus W, and an expanding gas has negative W. Check that your course materials use the same convention.
How do I find work from a PV diagram?
Find the area under the curve between the starting and ending volumes. Give it a negative sign if the gas expands.
Does the temperature always rise when heat is added?
No. If the gas does enough work as it expands, the internal energy can stay the same or even fall.
Do I need to know the equation for entropy?
No. Entropy is covered qualitatively in this course.
Where can I find the official scoring rules?
Exam formats change a little from year to year, so check the current course and exam description on the College Board site before test day.
Keep practicing
Every lesson in the AP Physics 2 course ends with practice items and an Exam focus box, and every unit has a ten-question practice set with worked answers. These free lessons also build the skills the free-response section tests:
- Free lesson 9.6: PV diagrams, work and thermodynamic processes
- Free lesson 9.5: internal energy and the first law
See the AP Physics 2 course Free lessons and lesson list
Other free-response guides:
- AP Physics 2 FRQ Guide: Free-Response Habits for Circuits, Gases, Optics and Modern Physics
- AP Physics 2 Experimental Design Explained: Planning an Experiment and Analyzing the Data
AP is a registered trademark of the College Board, which is not affiliated with and does not endorse this site. This guide is our own explanation of the question types and scoring. For the official scoring guidelines, see the College Board.