1. What is Isothermal Compressibility?

Isothermal compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change at constant temperature. It quantifies how much a substance compresses under pressure while maintaining a constant temperature.

2. How Does the Calculator Work?

The calculator uses the isothermal compressibility formula:

Where:

• \( K_T \) — Isothermal compressibility (m²/N)
• \( v \) — Specific volume (m³/kg)
• \( T \) — Temperature (K)
• \( \alpha \) — Coefficient of thermal expansion (1/K)
• \( \delta C_pv \) — Difference in heat capacities (J/kg·K)

Explanation: This formula relates the isothermal compressibility to thermodynamic properties including specific volume, temperature, thermal expansion coefficient, and the difference between heat capacities at constant pressure and volume.

3. Importance of Isothermal Compressibility

Details: Isothermal compressibility is a fundamental thermodynamic property used in various engineering applications, including fluid dynamics, material science, and chemical process design. It helps in understanding how materials behave under pressure and is crucial for designing systems that involve compression and expansion processes.

4. Using the Calculator

Tips: Enter specific volume in m³/kg, temperature in Kelvin, coefficient of thermal expansion in 1/K, and difference in heat capacities in J/kg·K. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of isothermal compressibility?
A: Isothermal compressibility indicates how easily a substance can be compressed under pressure while maintaining constant temperature. Higher values indicate greater compressibility.

Q2: How does temperature affect isothermal compressibility?
A: Generally, isothermal compressibility increases with temperature for most fluids, meaning they become more compressible as temperature rises.

Q3: What is the relationship between isothermal and adiabatic compressibility?
A: Isothermal compressibility is typically greater than adiabatic compressibility because temperature changes during adiabatic compression affect the compressibility.

Q4: Why is the difference in heat capacities important in this formula?
A: The difference between heat capacities at constant pressure and volume (δCpv) represents the energy required for volume expansion against external pressure.

Q5: What are typical values of isothermal compressibility for common substances?
A: Water has an isothermal compressibility of about 4.6×10⁻¹⁰ m²/N at 20°C, while gases have much higher compressibility values typically in the range of 10⁻⁵ to 10⁻⁶ m²/N.