Cycle Input Form
Formula Used
First law for each process: Q = ΔU + W
Ideal gas internal energy: ΔU = n Cv (T₂ - T₁)
Complete cycle rule: ΣΔU = 0, so Qnet = Wnet
Isobaric work: W = nR(T₂ - T₁)
Isothermal ideal gas work: W = nRT ln(V₂ / V₁)
Adiabatic path: Q = 0, so W = -ΔU
Polytropic path: W = nR(T₂ - T₁)/(1 - k), when exponent k ≠ 1
Thermal efficiency: η = Wnet / Qin × 100%
How to Use This Calculator
- Enter the gas amount, gas constant, and constant-volume heat capacity.
- Add the four state temperatures in kelvin.
- Add the four state volumes in cubic meters.
- Enter pressures in kilopascals when you want a P-V area check.
- Select a process type for each cycle leg.
- Use a polytropic exponent only for polytropic paths.
- Use custom work when measured or supplied work is known.
- Press the calculate button and read the result above the form.
- Download the process table as CSV or PDF when needed.
Example Data Table
| State | Temperature (K) | Volume (m³) | Pressure (kPa) | Next process |
|---|---|---|---|---|
| 1 | 500 | 0.020 | 207.86 | Isochoric heating |
| 2 | 800 | 0.020 | 332.58 | Isothermal expansion |
| 3 | 800 | 0.060 | 110.86 | Isochoric cooling |
| 4 | 500 | 0.060 | 69.29 | Isothermal compression |
Understanding Heat in a Thermodynamic Cycle
A thermodynamic cycle returns a system to its starting state. The pressure, volume, and temperature may change during each process. Yet the final internal energy equals the initial internal energy. This idea makes cycle heat easier to track. Heat is not stored inside the gas. It crosses the system boundary during selected steps. Work also crosses that boundary. The first law links both transfers.
Why Net Heat Matters
For a complete cycle, total internal energy change is zero. Therefore net heat equals net work. A heat engine uses positive net heat input to deliver useful work. A refrigerator needs work input to move heat from a cold region. A heat pump also needs work input. It focuses on useful heat delivered to a warm region. The sign of net work tells which device behavior is being modeled.
Process Details
Each path has its own heat rule. An isochoric path has no boundary work. Heat only changes internal energy. An isobaric path includes pressure-volume work. An isothermal ideal gas path often keeps internal energy nearly constant. Its heat is close to the work. An adiabatic path has no heat transfer. Work changes internal energy instead. A polytropic path uses an exponent. It can represent many real compression and expansion trends.
Using Ideal Gas Inputs
The calculator uses mole amount, gas constant, heat capacity, state temperatures, and state volumes. These inputs estimate internal energy change and boundary work. The optional pressure-volume points give a second work estimate. That method treats each path as a straight segment on a P-V diagram. It is useful for lab sketches and measured data. Differences between both methods show model mismatch.
Reading the Results
Positive heat means heat enters the working substance. Negative heat means heat leaves it. Positive work means the system does work on the surroundings. Negative work means work is done on the system. Heat input is the sum of positive heat steps. Heat rejected is the magnitude of negative heat steps. Efficiency is net work divided by heat input. For reversed cycles, coefficient of performance is often more useful than efficiency.
Common Accuracy Notes
Use absolute temperature in kelvin. Use volumes in cubic meters. Enter pressure points in kilopascals when using the P-V area option. Keep the sign convention consistent. Do not mix work done by the system with work done on the system. For real gases, ideal gas formulas are approximations. For large pressure ranges, property tables may be better. This tool is best for physics study, design screening, and cycle comparison.
Practical Interpretation
When the calculated cycle has positive net work, it behaves like an engine. When net work is negative, it behaves like a driven device. The closure error helps check the state data. A small value supports a complete cycle. A large value warns that one or more states need revision carefully now.
FAQs
What does positive heat mean?
Positive heat means energy enters the working substance as heat. It may raise internal energy, produce boundary work, or both. The exact split depends on the selected process path.
Why should net internal energy be zero?
A complete cycle returns to the original thermodynamic state. Internal energy is a state property. Its final and initial values match, so the total change should be zero.
What sign convention is used?
Work is positive when done by the system. Heat is positive when added to the system. This matches the form Q = ΔU + W used here.
Can I use this for a Carnot cycle?
Yes. Set two isothermal processes and two adiabatic processes. Enter matching temperatures and volumes. The result will estimate heat input, heat rejection, work, and efficiency.
What is the P-V area result?
It is an approximate cycle work from pressure and volume points. The calculator connects the points with straight segments. It is useful for rough diagram-based work estimates.
Why can process heat and P-V work differ?
They use different assumptions. Process heat uses ideal gas path formulas. P-V work uses straight-line pressure-volume segments. Real cycles may need more detailed property data.
Which heat capacity should I enter?
Enter constant-volume heat capacity in J/mol·K. For air near room temperature, a common estimate is about 20.8 J/mol·K. Use better data when available.
What does heat rejected mean?
Heat rejected is the magnitude of all negative heat transfers. It represents heat leaving the working substance during cooling, compression, or exhaust-related steps.
How is efficiency calculated?
Efficiency is net work output divided by heat input. It is shown only when the cycle produces positive net work and has positive heat input.
What is COP in the results?
COP is coefficient of performance. It is useful when net work is negative. Cooling COP uses heat absorbed divided by work input. Heating COP uses heat rejected divided by work input.
Can this replace property tables?
No. It is an idealized study calculator. Steam, refrigerants, phase changes, and real gas cycles often require property tables or validated simulation tools.