Calculator Form
Sign convention: use heat transfer positive to the system. Use work input and work output in separate fields. Keep all exergy rates in kW.
Example Data Table
| Case | Method | T0 (K) | Key Input | Computed Ṡgen | Computed ĖD |
|---|---|---|---|---|---|
| Case A | Direct entropy | 298.15 | Ṡgen = 0.1200 kW/K | 0.1200 kW/K | 35.7780 kW |
| Case B | Control-volume entropy | 300.00 | dScv/dt = 0.01, net balance gives Ṡgen = 0.0600 | 0.0600 kW/K | 18.0000 kW |
| Case C | Exergy balance | 298.15 | Ėx,in + Ėx,Q - Ėx,out - Ẇout = 40.0000 | 0.1342 kW/K | 40.0000 kW |
Formula Used
1) Direct Entropy Method
Exergy destruction rate: ĖD = T0 × Ṡgen
T0 is the environmental reference temperature in Kelvin. Ṡgen is the entropy generation rate. This is the fastest route when entropy generation is already known from testing or prior analysis.
2) Control-Volume Entropy Balance
Entropy generation rate: Ṡgen = dScv/dt - Σ(ṁin sin) + Σ(ṁout sout) - Σ(Q̇j/Tbj)
Then: ĖD = T0 × Ṡgen
Use this method when you know inlet and outlet entropy rates, accumulation, and heat transfer at known boundary temperatures.
3) Exergy Balance Method
Exergy destruction rate: ĖD = Ėx,in + Ėx,Q + Ẇin - Ėx,out - Ẇout - dExcv/dt
Heat exergy transfer: Ėx,Q = (1 - T0/Tb) × Q̇
This method is useful when aggregated exergy rates are known directly for streams, work, and heat interactions.
Important Sign Note
Enter heat positive to the system. Keep work input and work output separate. Negative results usually mean a sign convention issue, unit mismatch, or inconsistent field data.
How to Use This Calculator
- Select the calculation mode that matches your available data.
- Choose the temperature unit used for ambient and boundary temperatures.
- Enter the required entropy, exergy, flow, heat, and work terms.
- Use positive heat rates for heat entering the system.
- Optionally add reference, fuel, and product exergy rates for performance indicators.
- Press the calculate button to display the result above the form.
- Download the output as CSV or PDF when needed.
FAQs
1) What does exergy destruction rate represent?
It measures useful energy potential lost because of irreversibility. Higher values usually mean stronger second-law losses from friction, mixing, finite temperature heat transfer, throttling, or chemical irreversibility.
2) Why is ambient temperature required?
Exergy is defined relative to the environment. The ambient or dead-state temperature sets the reference for destroyed exergy, especially through the relation ĖD = T0 × Ṡgen.
3) Why can the result become negative?
A negative value usually means inconsistent signs, wrong temperature units, or mixed bases for exergy and entropy data. Review whether heat direction, work direction, and reference state assumptions match each other.
4) Which method should I choose?
Use the direct method when entropy generation is already known. Use the entropy balance when stream and heat data are available. Use the exergy balance when you know aggregated exergy rates directly.
5) What units should I use for specific entropy?
Use kJ/kg·K for specific entropy when mass flow is in kg/s. Then ṁ × s becomes kW/K, which fits the control-volume entropy balance used by this calculator.
6) Can I use this for turbines, compressors, or heat exchangers?
Yes. The calculator works for many steady or unsteady control volumes, including turbines, compressors, throttling valves, heat exchangers, condensers, boilers, and similar thermal systems.
7) What is the loss share versus reference?
It compares exergy destruction rate against a selected reference exergy rate. This helps benchmark how large the irreversibility is relative to fuel exergy, inlet exergy, or another design target.
8) Why include second-law efficiency fields?
They help connect destruction rate with overall usefulness. A system can have acceptable first-law performance while still wasting significant work potential through large second-law losses.