1. What Is a P–V Diagram?
A P–V diagram is a graph that shows how the pressure (P) of a gas changes with its volume (V) during a thermodynamic process. It helps visualize what is happening to a system when it expands, compresses, or undergoes other processes.
Each point on the graph represents a particular state of the system.
2. Why We Use P–V Diagrams
P–V diagrams make it easy to understand thermodynamic processes. They show how pressure and volume change and help calculate work done, since work is related to the area under the curve.
2.1. Benefits of P–V Diagrams
- Clear visualization of expansion and compression.
- Easy to compare different processes.
- Work done can be interpreted graphically.
- Useful for studying cycles like engines.
3. Work Done from a P–V Diagram
Work done in a thermodynamic process is given by the area under the P–V curve:
\( W = \int_{V_1}^{V_2} P \, dV \)
On a P–V graph, expansion corresponds to movement toward larger volumes, and compression corresponds to movement toward smaller volumes.
3.1. Expansion Work
During expansion, the curve moves to the right (toward higher volume). The area under the curve represents positive work done by the gas.
3.2. Compression Work
During compression, the curve moves to the left (toward lower volume). The area under the curve represents work done on the gas.
4. P–V Curves for Different Thermodynamic Processes
Each thermodynamic process has a characteristic P–V curve. These curves help identify what kind of process is taking place.
4.1. Isothermal Process (\(PV = \text{constant}\))
Temperature remains constant. The curve slopes downward smoothly. Work done is relatively high because volume changes significantly.
4.2. Adiabatic Process (\(PV^{\gamma} = \text{constant}\))
No heat exchange. The curve drops more steeply than an isothermal curve since pressure falls faster.
4.3. Isobaric Process (\(P = \text{constant}\))
Pressure remains constant. The P–V graph is a horizontal line. Work done is the rectangular area under the line.
4.4. Isochoric Process (\(V = \text{constant}\))
Volume remains constant. The P–V graph is a vertical line. No work is done because there is no change in volume.
5. Cyclic Processes on a P–V Diagram
A cyclic process is one in which the system eventually returns to its initial state. On a P–V diagram, this appears as a closed loop.
5.1. Work in a Cycle
The work done in a cycle is the area enclosed by the loop:
- If the cycle moves clockwise, the net work done is positive (typical for heat engines).
- If the cycle moves anticlockwise, the net work done is negative (typical for refrigerators).
6. Interpreting P–V Curves in Real Life
P–V diagrams help explain the functioning of engines, compressors, and refrigerators. Each part of a cycle corresponds to a real physical step such as compression, expansion, heating, or cooling.
6.1. Examples
- Internal combustion engines show distinct expansion and compression strokes on a P–V diagram.
- Steam power plants use P–V cycles to understand turbine work.
- Air compressors follow compression lines similar to isothermal or adiabatic curves.