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Entropy Change Calculator For Ideal Gases

Entropy Change Calculator for Gas Mixing

Entropy Change Calculator computes the entropy change when mixing two ideal gases. Select the gas types, input the number of moles for each gas, and calculate the entropy change.

Gas Types

Enter Parameters

How to Use Entropy Change Calculator:

  1. Select the types of the two gases (e.g., Nitrogen, Oxygen, Argon).
  2. Enter the number of moles for each gas using the keypad or direct input; use “Next” to switch fields.
  3. Click “Calculate” to see step-by-step results.
  4. Use “Share Result” to get shareable text or “Copy Result” to copy to clipboard.

Formulas:

Entropy Change (ΔS):

ΔS = -R (n₁ ln(x₁) + n₂ ln(x₂))

Mole Fractions:

x₁ = n₁ / (n₁ + n₂), x₂ = n₂ / (n₁ + n₂)

Where: R = universal gas constant (8.314 J/(mol·K)), n₁, n₂ = moles of gas 1 and 2, x₁, x₂ = mole fractions

Important Notes:

  • Inputs for moles of gas 1 and 2 must be positive numbers. Invalid inputs will trigger an error.
  • The two gases must be different for a meaningful entropy calculation.
  • The calculator assumes ideal gas behavior and constant temperature/pressure.
  • Clipboard access requires a secure context (HTTPS). If copying fails, try accessing over HTTPS or copy manually.

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Entropy Change Calculator

Entropy Change Calculator computes the entropy change (\\(\Delta S\\)) for a reversible process, such as heating a substance or an isothermal process, based on heat transfer, temperatures, and heat capacity.

Formulas Used in Entropy Change Calculator

The calculator computes entropy change based on the process type:

Heating (Constant \\(C_p\\)):

\\[ \Delta S = C_p \ln\left(\frac{T_2}{T_1}\right) \\]

Isothermal Process:

\\[ \Delta S = \frac{q}{T} \\]

Temperature Conversions:

\\[ T_K = T_C + 273.15 \\] \\[ T_K = \frac{5(T_F – 32)}{9} + 273.15 \\]

Where:

  • \\(\Delta S\\): Entropy change (kJ/(mol·K))
  • \\(C_p\\): Molar heat capacity at constant pressure (kJ/(mol·K))
  • \\(q\\): Heat added (kJ)
  • \\(T_1, T_2\\): Initial and final temperatures (K)
  • \\(T\\): Temperature for isothermal process (K)
  • \\(T_C\\): Temperature in Celsius (°C)
  • \\(T_F\\): Temperature in Fahrenheit (°F)

Example Calculation

Example: Heating with \\(C_p = 0.075 \, \text{kJ/(mol·K)}, T_1 = 298 \, \text{K}, T_2 = 373 \, \text{K}\\)

Compute: \\(\Delta S = 0.075 \ln\left(\frac{373}{298}\right)\\)

Result: \\(\Delta S \approx 0.017 \, \text{kJ/(mol·K)}\\)

Example: Isothermal with \\(q = 100 \, \text{kJ}, T = 298 \, \text{K}\\)

Compute: \\(\Delta S = \frac{100}{298}\\)

Result: \\(\Delta S \approx 0.336 \, \text{kJ/(mol·K)}\\)

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