Entropy Change Ideal Gas⚠ unverified
Physics / Thermodynamics · Compute the entropy change of an ideal gas between two states
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| m | m | kg | 1.0 | Mass of the gas |
| cv | cv | — | 1.0 | Specific heat at constant volume, in joules per kilogram-kelvin (J/(kg.K)) |
| T2 | T2 | K | 1.0 | Absolute temperature at state 2 |
| T1 | T1 | K | 1.0 | Absolute temperature at state 1 |
| R | R | — | 1.0 | Specific gas constant, in joules per kilogram-kelvin (J/(kg.K)) |
| v2 | v2 | m^3/kg | 1.0 | Specific volume at state 2 |
| v1 | v1 | m^3/kg | 1.0 | Specific volume at state 1 |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | ΔS | J/K | Entropy change, in joules per kelvin (J/K) |
The science & history
Understanding the Parameters
- $T$, $v$ — state variables; ratios are dimensionless so logarithms are valid. Use absolute $T$.
-
$c_v$, $R$ — live calculator labels them dimensionless; both need J/(kg·K) (or consistent molar forms with $m$ in kmol).
-
$\Delta S$ — state function for an ideal gas between two states (path independent).
Derivation (Approaching a Proof)
From $T\,ds = du + p\,dv$ and $du = c_v\,dT$, $p = \rho R T = R T / v$ (specific),
$$ds = c_v\frac{dT}{T} + R\frac{dv}{v}.$$
Integrate with constant $c_v$, $R$ between states 1 and 2; multiply by mass $m$ for total $\Delta S$.
History
Clausius’s entropy and ideal-gas integrations are core 19th-century thermodynamics; this $T$–$v$ formula is standard textbook material.
Related Concepts: Second Law Entropy, First Law DeltaU, Exergy Destruction, Speed Of Sound
Notes: Registry calculator entropy-change-ideal-gas (unverified). Unit bugs: $c_v$ and $R$
labelled dimensionless. Constant-$c_v$ ideal gas only.