Ideal gas, constant temperature
Enter State Values
The entered reference molar entropy must belong to the same temperature as the target state.
Example Data Table
| Sₘ₁ | P₁ | P₂ | n | ΔSₘ | Sₘ₂ |
|---|---|---|---|---|---|
| 191.61 J mol⁻¹ K⁻¹ | 1 atm | 2 atm | 1 mol | −5.763 J mol⁻¹ K⁻¹ | 185.847 J mol⁻¹ K⁻¹ |
| 191.61 J mol⁻¹ K⁻¹ | 2 bar | 0.5 bar | 3 mol | 11.526 J mol⁻¹ K⁻¹ | 203.136 J mol⁻¹ K⁻¹ |
Examples use an ideal gas and R = 8.314462618 J mol⁻¹ K⁻¹.
Formula Used
For an ideal gas moving between two pressures at constant temperature:
P₁ and P₂ must use the same pressure basis. The calculator converts selected units to pascals before calculating the ratio.
How to Use This Calculator
- Enter the known molar entropy at the reference pressure.
- Enter the reference pressure and select its unit.
- Enter the target pressure and select its unit.
- Add the gas amount in moles for total entropy outputs.
- Enter the matching absolute temperature in kelvin.
- Keep the default gas constant or enter a justified value.
- Select Calculate Entropy and review the pressure ratio first.
- Use CSV or PDF download after confirming the assumptions.
Entropy and Pressure
What Entropy Describes
Entropy measures how energy and arrangements spread through a system. Gas pressure changes can alter that spread even when temperature stays fixed. Lower pressure gives molecules more available space. Higher pressure restricts the accessible volume. For an ideal gas, this effect has a logarithmic form. The calculator applies that relationship to a reference state. It reports molar and total results.
Reference and Target States
A nonstandard pressure is a pressure different from the reference pressure. The reference may be one atmosphere, one bar, or another documented value. The important point is consistency. Enter both pressures with their units. The calculator converts each value to pascals before comparing them. This avoids false results caused by mixing bar, kilopascals, atmospheres, or millimetres of mercury during calculations.
Direction of the Entropy Change
The pressure correction uses the logarithm of the pressure ratio. When target pressure exceeds reference pressure, the logarithm is positive. The entropy correction becomes negative. Compression lowers ideal-gas entropy at constant temperature. When target pressure is lower, the correction becomes positive. Expansion raises entropy. Change size depends on the gas constant and amount. The formula does not depend on temperature.
Why Temperature Is Included
Temperature matters when you use a reference entropy value. Reference entropy must match the target temperature. This calculator asks for temperature to document that condition. It does not use temperature inside the isothermal pressure correction. A temperature change needs heat-capacity information. Do not combine temperature changes with this pressure-only model unless you calculate each contribution separately. Then combine terms carefully.
Molar and Total Results
Molar entropy uses joules per mole kelvin. It describes one mole of material. Total entropy uses joules per kelvin. It scales with entered moles. The calculator finds the molar pressure correction. It then multiplies that correction by amount. This makes the output useful for laboratory samples, process vessels, and textbook problems. Check the amount before using total entropy for decisions.
Limits of the Ideal-Gas Model
Real gases can depart from ideal behavior, at high pressure or near condensation. In those cases, pressure alone may not describe the entropy correction accurately. Fugacity is often used instead of pressure for rigorous work. Mixtures need composition data. Calculation is best for dilute gases and teaching examples. Treat output as an ideal-gas estimate unless equation of state supports conditions.
Checking Input Quality
Use significant figures in pressures. A small pressure difference creates an entropy correction. Rounding too early can hide result. Keep the reference entropy basis throughout the calculation. Do not enter total entropy as though it were molar entropy. The displayed pressure ratio is a check. A ratio above one indicates compression. A ratio below one indicates expansion at constant temperature.
Using the Result Well
The result is a state difference, not a measure of spontaneity. Entropy is one part of thermodynamic analysis. Gibbs energy depends on enthalpy and temperature. Still, pressure entropy corrections are essential in equilibrium, gas handling, and chemical potential work. Record reference pressure, temperature, gas model, and amount with every result. Clear assumptions make later checking faster, safer, and more reliable.
Frequently Asked Questions
What does nonstandard pressure mean?
It means the gas pressure differs from the reference state used for entropy. The reference may be one atmosphere, one bar, or a measured process pressure.
Which equation does this calculator use?
It uses the ideal-gas isothermal pressure relation: ΔSₘ = −R ln(P₂/P₁). It then adds that correction to reference molar entropy and scales it by moles.
Why does higher pressure reduce entropy?
At constant temperature, compression gives ideal-gas molecules less accessible volume. Fewer positional arrangements are available, so the entropy correction is negative.
Why is temperature entered?
The reference entropy must apply at the same temperature as the target state. Temperature documents the isothermal assumption, although it does not appear directly in this pressure-only correction.
Can I use atmospheres and bars together?
Yes. Select the correct unit beside each pressure. The calculator converts both values to pascals before forming the pressure ratio.
Does the calculator work for liquids?
Not reliably. The displayed equation is an ideal-gas relation. Liquids and solids usually need different property models because their volumes respond much less to pressure.
Can I calculate a total entropy change?
Yes. Enter the number of moles. The calculator multiplies the molar entropy correction by amount to give total entropy change in joules per kelvin.
What happens when target pressure is lower?
The pressure ratio becomes less than one. Its natural logarithm is negative, making the entropy correction positive. This matches ideal-gas expansion at constant temperature.
What gas constant should I enter?
Use 8.314462618 J mol⁻¹ K⁻¹ for standard SI work. Enter a custom positive value only when your data source requires a different consistent constant.
When is this result less accurate?
Accuracy falls at high density, near condensation, or for strongly nonideal mixtures. Rigorous work may require fugacity, composition data, and an equation of state.
Can this determine spontaneity?
No. Entropy change alone cannot determine spontaneity. Evaluate Gibbs energy using enthalpy, temperature, and all relevant system contributions.