Formula & Calculator
Change in Entropy (Reversible Process)
Calculates the change in entropy of a system undergoing a reversible heat transfer at constant absolute temperature.
Interpretation
Change in entropy for reversible process: ΔS = Q/T, where Q is heat transferred reversibly at temperature T. Entropy is a measure of disorder. Example: 100 J heat added at 300 K → ΔS = 0.333 J/K.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| delta_S | Change in entropy | J/K |
| Q | Heat transferred (reversibly) | J |
| T | Absolute temperature at which the transfer occurs | K |
What it means
Entropy change is defined for a reversible process as the ratio of the heat exchanged to the absolute temperature. This is a state function, meaning ΔS depends only on initial and final states. The second law of thermodynamics states that for any spontaneous process, the total entropy of the universe increases. Entropy is often described as a measure of disorder or randomness. The formula is used in thermodynamics to analyse heat engines, refrigerators, and chemical reactions. It is also crucial in statistical mechanics (Boltzmann formula S = k ln W). Understanding entropy and its changes is fundamental for energy conversion efficiency and for predicting the direction of processes.
Worked example
Change in Entropy – Two Examples
Real‑World| Parameter | Value |
|---|---|
| Q | 1000 J |
| T | 300 K |
| Parameter | Value |
|---|---|
| Q | -500 J |
| T | 250 K |
Common mistakes
- Reversible process: This formula applies to reversible processes only – for irreversible, ΔS > Q/T.
- Temperature T: In kelvin (absolute) – not Celsius.
- Heat Q: The heat transferred reversibly – in joules.
- Sign: Heat added to the system (positive Q) increases entropy; heat removed decreases entropy.
- Entropy is a state function: ΔS depends only on initial and final states, not the path – but the calculation of Q/T is path‑dependent for irreversible paths.
Applications
The change in entropy for a reversible process, ΔS = Q/T, is a central concept in thermodynamics. It quantifies the dispersal of energy and is used to assess the efficiency of heat engines, refrigerators, and chemical reactions. Engineers apply this equation to design power plants, to optimise refrigerators, and to evaluate the feasibility of processes. In materials science, it guides phase transformation studies. The formula is also essential in environmental engineering for analysing energy conversions. By understanding entropy change, professionals can identify irreversibilities, improve efficiency, and design sustainable energy systems.
- Design of heat engines and power cycles
- Refrigeration and air conditioning system analysis
- Chemical reaction feasibility and equilibrium studies
- Phase change analysis in materials
- Energy efficiency and environmental impact assessment
Frequently Asked Questions
For a reversible process at constant temperature, the change in entropy is ΔS = Q_rev / T, where Q_rev is the heat transferred reversibly and T is the absolute temperature. In general, for a reversible path, ΔS = ∫δQ_rev / T.
Applying it directly to an irreversible process. Entropy is a state function, so ΔS for an irreversible process is the same as for a reversible path connecting the same states, but the formula requires using the reversible heat.
In SI, the unit is J/K.
Since Q = 0, ΔS = 0. Such a process is called isentropic.
The entropy of an isolated system never decreases; it either remains constant (reversible) or increases (irreversible).
Boltzmann's entropy formula: S = k_B·ln W. This connects macroscopic entropy to microscopic disorder.
For an isothermal expansion from V₁ to V₂, ΔS = nR·ln(V₂/V₁). This is positive for expansion (increase in disorder).
- Determining the direction of spontaneous processes.
- Design of heat engines and refrigerators.
- Chemical equilibrium calculations.