Specific Volume Of Real Gas Given Heat Capacities Calculator

Formula Used:

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

Heat Capacity Constant Pressure (C_p):

J/kg·K

Heat Capacity Constant Volume (C_v):

J/kg·K

Isothermal Compressibility (K_T):

m²/N

Temperature (T):

Coefficient of Thermal Expansion (α):

1/K

Specific Volume (v):

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1. What is Specific Volume of Real Gas?

Specific Volume of a real gas is the volume occupied by a unit mass of the gas. It is the reciprocal of density and provides important thermodynamic information about the gas behavior under different conditions.

2. How Does the Calculator Work?

The calculator uses the thermodynamic formula:

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

Where:

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

Explanation: This formula relates the specific volume to fundamental thermodynamic properties through the relationship between heat capacities, compressibility, and thermal expansion.

3. Importance of Specific Volume Calculation

Details: Accurate calculation of specific volume is crucial for thermodynamic analysis, process design in chemical engineering, gas storage and transportation systems, and understanding gas behavior under various pressure and temperature conditions.

4. Using the Calculator

Tips: Enter all values in appropriate units. Heat capacities in J/kg·K, isothermal compressibility in m²/N, temperature in Kelvin, and thermal expansion coefficient in 1/K. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between C_p and C_v?
A: C_p is the heat capacity at constant pressure, while C_v is at constant volume. For ideal gases, C_p - C_v = R (gas constant).

Q2: What does isothermal compressibility represent?
A: Isothermal compressibility measures how much a substance's volume changes with pressure at constant temperature.

Q3: Why is thermal expansion coefficient important?
A: The thermal expansion coefficient indicates how much a material expands per degree of temperature increase.

Q4: What are typical values for specific volume of gases?
A: Specific volume varies greatly with pressure and temperature. At STP, air has specific volume of approximately 0.773 m³/kg.

Q5: When is this formula particularly useful?
A: This formula is especially valuable for real gas calculations where ideal gas assumptions don't apply, particularly at high pressures or low temperatures.