1. What is the Isothermal Expansion Equation?

The Isothermal Expansion equation calculates the work done during an isothermal expansion process where temperature remains constant. It's derived from the ideal gas law and thermodynamics principles.

2. How Does the Calculator Work?

The calculator uses the Isothermal Expansion equation:

Where:

• \( N_{KE} \) — Number of moles given KE
• \( 8.314 \) — Universal gas constant (J/mol·K)
• \( T_{high} \) — High temperature (K)
• \( V_f \) — Final volume (m³)
• \( V_i \) — Initial volume (m³)
• \( \ln \) — Natural logarithm function

Explanation: The equation calculates the work done during expansion at constant temperature, with the negative sign indicating work done by the system.

3. Importance of Isothermal Expansion Calculation

Details: Accurate calculation of work done in isothermal expansion is crucial for thermodynamic analysis, engine design, and understanding energy transfer in physical systems.

4. Using the Calculator

Tips: Enter number of moles, temperature in Kelvin, final volume, and initial volume. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: Why is the work negative in the equation?
A: The negative sign indicates that work is done by the system on the surroundings during expansion.

Q2: What is the significance of constant temperature?
A: Isothermal processes maintain constant temperature, which simplifies the work calculation and ensures internal energy remains constant for ideal gases.

Q3: What units should be used for volume?
A: Volume should be in cubic meters (m³) for consistency with SI units and the gas constant.

Q4: Can this equation be used for real gases?
A: This equation is derived for ideal gases. For real gases, additional correction factors may be needed.

Q5: What does the natural logarithm represent?
A: The natural logarithm accounts for the logarithmic relationship between work done and volume ratio in isothermal processes.