Estimate entropy production for thermal systems and flows. Choose a method, convert units, and verify each step. Build reliable physical intuition fast.
Entropy rate describes how fast entropy changes with time, often written as Ṡ = dS/dt. This tool supports three practical physics formulations:
Ṡ = Q̇ / T, where Q̇ is heat transfer rate and T is absolute temperature.Ṡ = (S₂ − S₁) / Δt, using measured entropy at two times.Ṡ = ṁ·s, where ṁ is mass flow rate and s is specific entropy.Sign convention matters: choose inputs consistently for inflow, outflow, or system change.
| Case | Method | Inputs | Entropy rate (J/(s·K)) |
|---|---|---|---|
| A | Q̇ / T | Q̇ = 1200 W, T = 350 K | 3.428571 |
| B | ΔS / Δt | S₁ = 2.50 J/K, S₂ = 3.10 J/K, Δt = 60 s | 0.010000 |
| C | ṁ·s | ṁ = 0.80 kg/s, s = 6.5 kJ/(kg·K) | 5200.000000 |
Entropy rate, written as Ṡ, quantifies how quickly entropy changes in time. In experiments and engineering, it is often reported in W/K, which is identical to J/(s·K). This calculator focuses on three practical pathways: heat transfer at a boundary, measured entropy change across a time window, and entropy transport by a flowing mass stream.
Entropy rate links directly to irreversibility and the Second Law. For a control volume, a useful balance is: accumulation = entropy in − entropy out + entropy generation. Large positive rates usually indicate strong dissipation, mixing, friction, chemical reactions, or heat transfer across finite temperature differences.
For near-reversible heat transfer at a boundary, Ṡ = Q̇/T. As a quick check, if Q̇ = 2.0 kW and T = 400 K, then Ṡ = 2000/400 = 5.0 W/K. If the same 2.0 kW occurs at 300 K, the rate rises to 6.67 W/K, showing how lower temperature increases entropy transfer per unit heat.
When you have entropy at two times, the average rate is Ṡ = (S₂ − S₁)/Δt. Example: S₁ = 1.20 kJ/K, S₂ = 1.32 kJ/K, and Δt = 10 min. Convert: ΔS = 0.12 kJ/K = 120 J/K and Δt = 600 s, so Ṡ = 0.20 W/K.
For steady flow, entropy transport is Ṡ = ṁ·s. If ṁ = 0.50 kg/s and s = 7.0 kJ/(kg·K), then Ṡ = 0.50 × 7000 = 3500 W/K. For net transport across a device, compute ṁ(sout − sin) using the same unit basis.
Define positive directions before calculating. For heat transfer, choose whether positive Q̇ is into or out of the system. For mass streams, treat inlet and outlet separately. A negative Ṡ from the finite-difference method simply means system entropy decreased during that interval; it does not violate the Second Law by itself.
Use absolute temperature in the heat-flow method. If sensors provide °C or °F, convert to K first. For transient studies, keep Δt small enough to capture dynamics but large enough to suppress noise. Report uncertainty: if Q̇ has ±3% error and T has ±1% error, Ṡ uncertainty is roughly ±4% by simple propagation.
Watch unit consistency: kJ/K and J/K differ by 1000, and minutes must be converted to seconds. Sanity check magnitudes: laboratory thermal processes often sit between 0.01 and 10 W/K, while industrial steam and large flow systems can reach 10³–10⁵ W/K. Use the intermediate-value cards to verify conversions.
Use J/(s·K) or W/K. They are equivalent because 1 W = 1 J/s. This calculator outputs SI so you can compare results across experiments.
The formula requires absolute temperature. Using °C or °F shifts the zero point and produces incorrect entropy rates. Convert to K before dividing heat rate by temperature.
Yes, for system entropy change over time, Ṡ can be negative if the system becomes more ordered during the interval. The total entropy of system plus surroundings must still satisfy the Second Law.
Compute each stream as ṁ·s and then subtract: net = Σ(ṁ·s)in − Σ(ṁ·s)out, using consistent units. This reveals whether entropy is carried into or away from the control volume.
Transfer moves entropy across boundaries via heat and mass. Generation is created internally by irreversibility such as friction, mixing, finite ΔT heat flow, or reactions. Generation is always non‑negative.
It gives an average rate over Δt. If entropy changes rapidly, reduce Δt or use a better time-resolved estimate. Measurement noise can dominate when ΔS is small compared with sensor uncertainty.
Confirm Kelvin temperature for heat mode, seconds for time, and kJ-to-J conversions. Then compare magnitude with typical ranges: small lab tests often yield 0.01–10 W/K, while large plants can be orders higher.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.