Isothermal Compressibility Given Molar Heat Capacity At Constant Pressure And Volume Calculator

Formula Used:

\[ K_T = \frac{C_p}{C_v} \times K_S \]

Molar Specific Heat Capacity at Constant Pressure (Cₚ):

J/(mol·K)

Molar Specific Heat Capacity at Constant Volume (Cᵥ):

J/(mol·K)

Isentropic Compressibility (Kₛ):

m²/N

Isothermal Compressibility (Kₜ):

Unit Converter ▲

Unit Converter ▼

From:	To:

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 formula:

\[ K_T = \frac{C_p}{C_v} \times K_S \]

Where:

\( K_T \) — Isothermal compressibility (m²/N)
\( C_p \) — Molar specific heat capacity at constant pressure (J/(mol·K))
\( C_v \) — Molar specific heat capacity at constant volume (J/(mol·K))
\( K_S \) — Isentropic compressibility (m²/N)

Explanation: This formula relates isothermal compressibility to the ratio of heat capacities and isentropic compressibility, providing a fundamental relationship in thermodynamics.

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 molar specific heat capacities at constant pressure and volume in J/(mol·K), and isentropic compressibility in m²/N. All values must be positive and non-zero for accurate calculation.

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: Why is the ratio Cₚ/Cᵥ important in this calculation?
A: The ratio Cₚ/Cᵥ (also known as the adiabatic index or heat capacity ratio) relates how a substance responds to compression under different thermodynamic conditions.

Q3: What are typical values for isothermal compressibility?
A: Values vary significantly by material. Gases have high compressibility (large values), while liquids and solids have much lower compressibility (small values).

Q4: How does temperature affect isothermal compressibility?
A: For most substances, compressibility increases with temperature as molecular interactions weaken and materials become more easily compressed.

Q5: What are practical applications of isothermal compressibility?
A: Applications include petroleum engineering (reservoir characterization), material science (characterizing material properties), and chemical engineering (process design involving compressible fluids).