Isothermal Compressibility Of Real Gas Calculator

Isothermal Compressibility Formula:

\[ K_T = \frac{v \cdot T \cdot \alpha^2}{C_p - C_v} \]

Specific Volume (v):

m³/kg

Temperature (T):

Coefficient of Thermal Expansion (α):

1/K

Heat Capacity Constant Pressure (Cp):

J/kg·K

Heat Capacity Constant Volume (Cv):

J/kg·K

Isothermal Compressibility (K_T):

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1. What is Isothermal Compressibility?

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

2. How Does the Calculator Work?

The calculator uses the isothermal compressibility formula:

\[ K_T = \frac{v \cdot T \cdot \alpha^2}{C_p - C_v} \]

Where:

\( K_T \) — Isothermal compressibility (m²/N)
\( v \) — Specific volume (m³/kg)
\( T \) — Temperature (K)
\( \alpha \) — Coefficient of thermal expansion (1/K)
\( C_p \) — Heat capacity at constant pressure (J/kg·K)
\( C_v \) — Heat capacity at constant volume (J/kg·K)

Explanation: This formula relates the compressibility of a real gas to its thermal properties and specific volume, providing insight into how the gas behaves under pressure changes at constant temperature.

3. Importance of Isothermal Compressibility

Details: Isothermal compressibility is crucial in thermodynamics and fluid mechanics for understanding how substances respond to pressure changes. It's particularly important in the study of real gases, petroleum engineering, and materials science where pressure-volume relationships are critical.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure that heat capacity at constant pressure (Cp) is greater than heat capacity at constant volume (Cv), and all input values are 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 constant temperature conditions. Higher values mean the substance is more compressible.

Q2: How does isothermal compressibility differ from adiabatic compressibility?
A: Isothermal compressibility measures volume change at constant temperature, while adiabatic compressibility measures volume change with no heat exchange.

Q3: What are typical values for isothermal compressibility?
A: Values vary widely depending on the substance. Gases have high compressibility (10⁻⁵ to 10⁻⁶ m²/N), while liquids and solids have much lower values (10⁻⁹ to 10⁻¹¹ m²/N).

Q4: Why must Cp be greater than Cv?
A: Cp is always greater than Cv because at constant pressure, some energy is used to do work by expanding the gas, requiring more heat input to achieve the same temperature change.

Q5: What are the limitations of this calculation?
A: This formula assumes ideal gas behavior and may not be accurate for substances with strong intermolecular forces or near phase transitions.