1. What is Boyle's Law and Isothermal Work?

Boyle's Law states that for a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional (P ∝ 1/V). In isothermal processes (constant temperature), the work done by the gas during expansion or compression can be calculated using the given equation.

2. How Does the Calculator Work?

The calculator uses the isothermal work equation:

Where:

• \( W \) — Work done by the gas (Joules)
• \( n \) — Number of moles of gas (mol)
• \( R \) — Universal gas constant (8.314 J/mol·K)
• \( T \) — Absolute temperature (Kelvin)
• \( V_1 \) — Initial volume (m³)
• \( V_2 \) — Final volume (m³)

Explanation: The equation calculates the work done during an isothermal expansion or compression of an ideal gas.

3. Importance of Work Calculation

Details: Calculating work in thermodynamic processes is essential for understanding energy transfer in systems, designing engines, and analyzing thermodynamic cycles.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure temperature is in Kelvin (K = °C + 273.15) and volumes are in cubic meters (1 L = 0.001 m³).

5. Frequently Asked Questions (FAQ)

Q1: Why is temperature constant in this calculation?
A: The equation assumes isothermal conditions where temperature remains constant throughout the process.

Q2: What's the significance of the natural logarithm in the equation?
A: The ln(V2/V1) term accounts for the continuous change in pressure as volume changes during the process.

Q3: Can this be used for real gases?
A: The equation is exact for ideal gases and reasonably accurate for real gases at low pressures and high temperatures.

Q4: What does negative work mean?
A: Negative work indicates work is done on the gas (compression) rather than by the gas (expansion).

Q5: How does this relate to Boyle's Law?
A: Boyle's Law (P₁V₁ = P₂V₂) describes the pressure-volume relationship, while this equation calculates the work done during the volume change.