A pressure volume diagram, or PV diagram, shows how the pressure and volume of a gas change during a thermodynamic process. It is one of the most useful tools for connecting graphs to physical quantities like work, heat, and internal energy. For an ideal gas, the shape of the path tells you what is being held constant and how energy is transferred.
Engineers and scientists use PV diagrams to analyze engines, refrigerators, pumps, and natural gas expansion.
On a PV diagram, the work done by the gas is the area under the curve, W = ∫P dV. Expansion gives positive work by the gas because volume increases, while compression gives negative work by the gas because volume decreases. The first law of thermodynamics, ΔU = Q - W, connects the graph to energy changes.
For an ideal gas, internal energy depends only on temperature, so processes with no temperature change have ΔU = 0.
Key Facts
- Ideal gas law: PV = nRT.
- Work done by a gas on a PV diagram: W = ∫P dV.
- For constant pressure: W = PΔV.
- First law of thermodynamics: ΔU = Q - W, where W is work done by the gas.
- For an ideal gas, internal energy depends only on temperature: ΔU = nCvΔT.
- Isothermal process: ΔT = 0 and ΔU = 0, so Q = W for an ideal gas.
Vocabulary
- PV Diagram
- A graph of pressure versus volume that shows the path of a gas during a thermodynamic process.
- Isothermal Process
- A thermodynamic process that occurs at constant temperature.
- Adiabatic Process
- A thermodynamic process in which no heat is transferred between the system and its surroundings.
- Isochoric Process
- A thermodynamic process that occurs at constant volume, so no work is done by the gas.
- Isobaric Process
- A thermodynamic process that occurs at constant pressure.
Common Mistakes to Avoid
- Confusing work done by the gas with work done on the gas. If the gas expands, W by the gas is positive, but work done on the gas is negative.
- Using W = PΔV for every process. This formula only works when pressure is constant, while curved paths require area under the curve or integration.
- Assuming heat and temperature change are the same thing. Heat is energy transferred across a boundary, while temperature is related to the average kinetic energy of particles.
- Thinking ΔU depends on the shape of the path for an ideal gas. Internal energy depends only on temperature change, so different paths with the same initial and final temperatures have the same ΔU.
Practice Questions
- 1 A gas expands at constant pressure 2.0 x 10^5 Pa from 0.030 m^3 to 0.080 m^3. How much work is done by the gas?
- 2 An ideal gas absorbs 600 J of heat while doing 250 J of work on its surroundings. What is the change in internal energy of the gas?
- 3 Two different paths connect the same initial and final states on a PV diagram. One path has a larger area under the curve than the other. Explain which path has more work done by the gas and whether the change in internal energy must be different.