Thermodynamics
Isothermal expansion — entropy change
Reversible isothermal expansion: ΔS = nR ln(V₂/V₁) = Q/T.
Isothermal expansion — entropy change — interactive Thermodynamics simulation. Reversible isothermal expansion: ΔS = nR ln(V₂/V₁) = Q/T. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Entropy change
Reversible isothermal expansion: ΔS = nR ln(V₂/V₁) = Q/T.
Entropy change measures how spread-out energy becomes. In a reversible isothermal expansion the gas absorbs heat Q while its temperature stays fixed, and entropy rises because the same energy occupies a larger volume with more microstates.
- ΔS = nR ln(V₂/V₁)
- ΔS = Q_rev/T
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
A gas expands isothermally and reversibly to a larger volume. Does its entropy increase, decrease, or stay the same?
Predictions to weigh
- Entropy decreases as the gas spreads out.
- Entropy stays constant since the process is reversible.
- Entropy increases — the gas has more possible microscopic arrangements at larger volume.
Variable roles
What you set:
- Final volume V₂ (L)
What you measure:
- Heat exchanged Q (J)
- Entropy change ΔS (J/K)
How the investigation runs
- Open the entropy-isothermal preset and press Reset. 1 mol of argon starts at 20 L, 300 K.
- Enable the heat-exchanged and entropy-change readouts.
- Set the target (final) volume for each trial, and record the heat exchanged and the entropy change.
Governing equation
Entropy Change in a Reversible Isothermal Process — ΔS = Q/T
For a reversible isothermal expansion, entropy change equals heat exchanged divided by the constant temperature, which works out to ΔS = nR·ln(V₂/V₁) for an ideal gas — entropy grows with the logarithm of the volume ratio.
What the printable worksheet asks students to work out
- For one trial, compute Q = nRT·ln(V₂/V₁) using n = 1 mol, R = 8.314 J/(mol·K), T = 300 K, then ΔS = Q/T (equivalently ΔS = nR·ln(V₂/V₁) directly). Compare both to the table.
- Explain why ΔS is positive in every trial here, and why a bigger expansion (larger V₂) produces a bigger entropy increase.
Where this shows up beyond the lab
- This experiment assumes a reversible (infinitely slow) expansion. A free (uncontrolled) expansion into vacuum to the same final volume would produce the exact same ΔS for the gas, even though no heat is exchanged at all (Q = 0) and no work is done. Explain why entropy is a state function that doesn't care how the gas got from V₁ to V₂.
- The second law says total entropy (gas plus surroundings) can never decrease for a real process. For this reversible isothermal expansion, the surroundings (the heat reservoir supplying Q) lose exactly as much entropy as the gas gains. Explain why that makes the total entropy change zero — the signature of a reversible process.
- AP Physics 2 — Unit 9: Thermodynamics
- IB Physics — B.4 Thermodynamics
- General High School Physics — Heat, temperature & gas laws
- NGSS High School Physics — Thermal energy transfer
- Welcome to Entropy Isothermal
- Select the chamber
- Press Play
- Entropy from volume change
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.