Pressure volume and temperature entropy diagrams are two of the most useful pictures in engineering thermodynamics. They turn changes in a gas, vapor, or working fluid into curves that show how pressure, volume, temperature, and entropy vary during a process. Engineers use these diagrams to analyze engines, turbines, compressors, refrigerators, and power plants.
The shape of the path and the area under or inside it can reveal useful work, heat transfer, and cycle performance.
On a P-V diagram, the area under a process curve represents boundary work, so expansion usually produces work and compression usually requires work input. On a T-S diagram, the area under a reversible process curve represents heat transfer, making it especially helpful for visualizing heat engines and refrigerators. A complete thermodynamic cycle returns to its starting state, so it appears as a closed loop on both diagrams.
Comparing the two diagrams helps engineers connect mechanical output with thermal energy flow and spot losses such as irreversibility and entropy generation.
Understanding Engineering: PV and TS Diagrams
A diagram represents a sequence of equilibrium states. This matters because pressure and temperature are properties of a state, while work and heat depend on the route taken between states. Two processes can begin and end at the same conditions yet require different amounts of work.
A slow compression that stays close to equilibrium can be drawn clearly. A rapid, turbulent compression is harder to represent by one smooth path.
Engineers often use ideal paths first because they make the energy accounting understandable. They then compare those paths with measured data from a real machine.
The most important feature on many temperature entropy plots is the saturation dome. Inside this dome, a substance exists as a liquid vapor mixture. The left boundary is saturated liquid, and the right boundary is saturated vapor.
Moving across the dome at constant pressure can represent boiling or condensation. Temperature remains nearly constant during this change for a pure substance at a fixed pressure, even though large amounts of energy enter or leave.
The vapor quality tells how much of the mixture is vapor by mass. Quality is especially important in steam turbines because liquid droplets can strike blades, reduce efficiency, and cause erosion.
Engineers add families of guide lines to diagrams to identify processes. A constant volume path is vertical on a pressure volume plot. A constant pressure path is horizontal.
On a temperature entropy plot, an ideal isentropic process is vertical because entropy stays constant. Turbine and compressor calculations often begin with this ideal process. Real fluid friction, heat leakage, shock waves, and mixing increase entropy.
This shifts the actual outlet state away from the ideal one. The difference helps define isentropic efficiency. A turbine with a larger actual entropy rise gives less useful work than an ideal turbine operating between the same inlet pressure and outlet pressure.
Students should read scales carefully before interpreting any curve. Pressure may be shown as absolute pressure or gauge pressure, and this choice changes numerical work calculations. Volume may mean total volume, specific volume per unit mass, or molar volume.
Temperature entropy diagrams normally require absolute temperature for energy calculations. It is useful to mark every state with known properties, then identify what remains constant during each step. Tables or software may be needed because water and refrigerants do not follow the simple ideal gas rules near saturation.
In classroom problems, state the assumptions clearly. Common assumptions include steady flow, negligible kinetic energy changes, and internally reversible behavior. These assumptions are not always true, but they show which physical effects a diagram is leaving out.
Key Facts
- P-V diagram axes: pressure P is on the vertical axis and volume V is on the horizontal axis.
- T-S diagram axes: temperature T is on the vertical axis and entropy S is on the horizontal axis.
- Boundary work for a quasi-equilibrium process is W = integral P dV.
- Reversible heat transfer on a T-S diagram is Q_rev = integral T dS.
- For a closed cycle, the net change in internal energy is Delta U = 0, so Q_net = W_net.
- A clockwise cycle on a P-V diagram usually represents a heat engine with net work output.
Vocabulary
- Pressure
- Pressure is the force exerted per unit area by a fluid, commonly measured in pascals or kilopascals.
- Volume
- Volume is the amount of space occupied by a system or working fluid, often measured in cubic meters.
- Entropy
- Entropy is a thermodynamic property that measures energy dispersal and helps track irreversibility in a process.
- Cycle
- A cycle is a sequence of thermodynamic processes that returns the system to its initial state.
- Boundary Work
- Boundary work is energy transfer caused by the moving boundary of a system during expansion or compression.
Common Mistakes to Avoid
- Confusing the area under a curve with the slope of the curve. On a P-V diagram, work comes from the area integral W = integral P dV, not from how steep the path looks.
- Assuming area on every T-S diagram always equals heat. The relation Q = integral T dS applies directly only for internally reversible heat transfer.
- Forgetting that a cycle must end at its starting state. If the path does not close, the process is not a complete cycle and net work or heat cannot be read as an enclosed area.
- Mixing up expansion and compression signs. On a P-V diagram, motion to the right means increasing volume and usually work output by the system, while motion to the left means work input to the system.
Practice Questions
- 1 A gas expands at a constant pressure of 300 kPa from 0.020 m^3 to 0.080 m^3. Find the boundary work in kJ.
- 2 During a reversible heating process, a substance receives heat at a constant temperature of 500 K while its entropy increases from 1.20 kJ/K to 1.75 kJ/K. Find the heat transfer in kJ.
- 3 A closed loop on a P-V diagram is traced clockwise, while the matching T-S diagram shows heat added at high temperature and rejected at low temperature. Explain whether the device behaves more like a heat engine or a refrigerator, and justify your answer using areas on the diagrams.