Isothermal Compressibility Given Thermal Pressure Coefficient And Cp Calculator

Formula Used:

\[ K_T = \frac{1}{\left(\frac{1}{K_S}\right) - \frac{(\Lambda^2 \times T)}{\rho \times (C_p - [R])}} \]

Isentropic Compressibility (K_S):

m²/N

Thermal Pressure Coefficient (Λ):

Pa/K

Temperature (T):

Density (ρ):

kg/m³

Molar Specific Heat Capacity at Constant Pressure (C_p):

J/K·mol

Isothermal Compressibility (K_T):

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1. What Is Isothermal Compressibility?

Isothermal compressibility is a thermodynamic property that measures the relative volume change of a substance in response to a pressure change at constant temperature. It quantifies how much a material compresses under pressure while maintaining a constant temperature.

2. How Does The Calculator Work?

The calculator uses the following formula:

\[ K_T = \frac{1}{\left(\frac{1}{K_S}\right) - \frac{(\Lambda^2 \times T)}{\rho \times (C_p - [R])}} \]

Where:

\( K_T \) — Isothermal compressibility (m²/N)
\( K_S \) — Isentropic compressibility (m²/N)
\( \Lambda \) — Thermal pressure coefficient (Pa/K)
\( T \) — Temperature (K)
\( \rho \) — Density (kg/m³)
\( C_p \) — Molar specific heat capacity at constant pressure (J/K·mol)
\( [R] \) — Universal gas constant (8.314 J/K·mol)

Explanation: This formula relates isothermal compressibility to other thermodynamic properties through fundamental thermodynamic relationships.

3. Importance Of Isothermal Compressibility Calculation

Details: Isothermal compressibility is crucial for understanding material behavior under pressure, designing pressure vessels, studying fluid dynamics, and analyzing thermodynamic processes in various engineering and scientific applications.

4. Using The Calculator

Tips: Enter all values in appropriate units. Ensure isentropic compressibility, temperature, density, and molar specific heat capacity are positive values. The thermal pressure coefficient should be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between isothermal and isentropic compressibility?
A: Isothermal compressibility measures volume change at constant temperature, while isentropic compressibility measures volume change at constant entropy (adiabatic process).

Q2: What are typical values for isothermal compressibility?
A: Values vary widely by material. For liquids, typically around 10⁻¹⁰ to 10⁻⁹ m²/N; for gases, much higher around 10⁻⁵ to 10⁻⁴ m²/N at standard conditions.

Q3: Why is the universal gas constant used in this formula?
A: The universal gas constant appears because the formula involves molar specific heat capacity, which is related to the gas constant through thermodynamic relationships.

Q4: Can this calculator be used for all materials?
A: This formula is generally applicable to gases and many liquids, but may have limitations for complex materials or extreme conditions.

Q5: What happens if C_p - [R] becomes zero or negative?
A: The denominator would become undefined or negative, which is physically unrealistic. C_p must be greater than [R] for valid results.