Heat Capacity At Constant Volume Of Real Gas Calculator

Formula Used:

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

Heat Capacity Constant Pressure (Cp):

J/kg·K

Specific Volume (v):

m³/kg

Temperature (T):

Coefficient of Thermal Expansion (α):

1/K

Isothermal Compressibility (K_T):

m²/N

Heat Capacity Constant Volume (C_v):

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1. What is Heat Capacity at Constant Volume?

Heat capacity at constant volume (C_v) is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Kelvin while keeping the volume constant. For real gases, it differs from the ideal gas value due to intermolecular forces.

2. How Does the Calculator Work?

The calculator uses the thermodynamic relation:

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

Where:

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

Explanation: This formula relates the difference between constant pressure and constant volume heat capacities to thermal expansion and compressibility properties of the substance.

3. Importance of Cv Calculation

Details: Accurate calculation of C_v is essential for thermodynamic analysis, energy balance calculations, and understanding the thermal behavior of real gases in various engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure temperature is in Kelvin, specific volume in m³/kg, and other parameters in their respective SI units. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Why is Cv different for real gases compared to ideal gases?
A: Real gases have intermolecular forces and molecular volume effects that cause deviations from ideal gas behavior, affecting their heat capacity values.

Q2: What are typical values for Cv in common gases?
A: For monatomic gases like helium, Cv is about 3/2 R; for diatomic gases like nitrogen, it's about 5/2 R; but these values change with temperature and pressure for real gases.

Q3: How does temperature affect Cv for real gases?
A: Cv generally increases with temperature for real gases due to the excitation of additional vibrational modes and changes in intermolecular interactions.

Q4: What are the limitations of this formula?
A: This formula assumes the substance follows certain thermodynamic relations and may not be accurate near phase transitions or critical points.

Q5: Can this calculator be used for liquids as well?
A: Yes, the same thermodynamic relation applies to liquids, though the parameter values will be significantly different from gases.