How do I get total entropy change?

Provide an ambient T_surr. We estimate ΔS_surr ≈ −q_sys/T_surr and report ΔS_total = ΔS_sys + ΔS_surr.

Entropy Calculator

Compute entropy changes ΔS for common thermodynamic processes: isothermal ideal-gas expansion/compression, heating/cooling with constant heat capacity, phase changes, and ideal-gas mixing. Shows steps and an optional ΔS mini chart (system, surroundings, total).

Background

Entropy change is defined by the reversible path heat divided by temperature, dS = δq_rev/T. For typical course problems we use standard models: ideal gases, constant heat capacities, and tabulated enthalpies for phase changes. When possible, we also estimate surroundings’ entropy to illustrate the second law via ΔS_total = ΔS_sys + ΔS_surr.

Choose a mode and enter values

Mode:

Isothermal ideal gas (ΔS = nR ln(V₂/V₁) = nR ln(P₁/P₂))

Heating/Cooling at constant heat capacity (ΔS = C ln(T₂/T₁))

Phase change at constant T (ΔS = ΔH_trans/T)

Ideal-gas mixing (two components)

Options:

Step-by-step working

Mini chart: ΔS_sys, ΔS_surr, ΔS_total

Round to sensible significant figures

Surroundings (optional):

If provided, we estimate ΔS_surr ≈ −q_sys/T_surr and report ΔS_total.

Given:

ΔS = nR ln(V₂/V₁) = nR ln(P₁/P₂). Use ratio > 0.

Quick picks:

Chips prefill fields; you can edit and recalculate.

Result:

No results yet. Choose a mode and enter values.

How to use this calculator

Isothermal: enter moles and a valid ratio (V₂/V₁ or P₁/P₂).
Heating/Cooling: pick Cp/Cv/Custom C, set basis (per mol/gram/total), provide T₁, T₂, and amount if needed.
Phase change: enter n, ΔH_trans (kJ·mol⁻¹), and T (K).
Mixing: give n₁ and n₂ (ideal gases). We compute xᵢ and ΔS_mix.
Surroundings (optional): set T_surr to estimate ΔS_surr and ΔS_total.

Units: T in K; R = 8.314462618 J·mol⁻¹·K⁻¹; natural logarithms.

Formula & Equation Used

Isothermal ideal gas:

ΔS = n R ln (\frac{V_{2}}{V_{1}}) = n R ln (\frac{P_{1}}{P_{2}}), T constant

Heating/Cooling (constant heat capacity):

ΔS = C ln (\frac{T_{2}}{T_{1}}), C = nCₚ, nCᵥ, mc, or total

Phase change at constant T:

ΔS = n {ΔH}_{trans} / T

Ideal-gas mixing (two components):

{ΔS}_{mix} = - R \sum n_{i} ln x_{i}, xᵢ = nᵢ / (n₁ + n₂)

Surroundings and total:

{ΔS}_{surr} \approx - q_{sys} / T_{surr}, ΔS = {ΔS}_{sys} + {ΔS}_{surr}

Example Problems & Step-by-Step Solutions

Example 1 — Isothermal expansion

n=1.00 mol ideal gas expands isothermally with V₂/V₁=2.00.
ΔS = nR ln(2.00) = 1.00×8.314×0.693 = 5.76 J·K⁻¹. (q>0 to system; if T_surr=T, ΔS_total=0.)

Example 2 — Heating at constant Cp

Cp=75.3 J·mol⁻¹·K⁻¹, n=1.00 mol, T: 298→350 K.
C = n·Cp = 75.3 J·K⁻¹; ΔS = 75.3 ln(350/298) = 11.7 J·K⁻¹.

Example 3 — Vaporization

n=0.500 mol, ΔH_vap=40.65 kJ·mol⁻¹, T=373.15 K.
ΔS = n·ΔH/T = 0.500×40650/373.15 = 54.5 J·K⁻¹.

Frequently Asked Questions

Q: Should I use natural or base-10 logs?

Use natural logarithms (ln). The gas constant is in J·mol⁻¹·K⁻¹.

Q: Can I enter temperatures in °C?

Please convert to Kelvin: T(K)=T(°C)+273.15.

Q: How do I get ΔS_total?

Provide an ambient T_surr. We estimate ΔS_surr≈−q_sys/T_surr for the modeled reversible path.

Temperature