Heat Capacity At Constant Pressure Of Real Gas Calculator

Heat Capacity Constant Pressure Formula:

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

Specific Volume (v):

m³/kg

Temperature (T):

Coefficient of Thermal Expansion (α):

1/K

Isothermal Compressibility (Kₜ):

m²/N

Heat Capacity Constant Volume (Cᵥ):

J/kg·K

Heat Capacity Constant Pressure (Cₚ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Heat Capacity at Constant Pressure?

Heat capacity at constant pressure (Cₚ) is the amount of heat energy required to raise the temperature of a unit mass of a substance by one degree Kelvin while maintaining constant pressure. It's a crucial thermodynamic property for real gases and other substances.

2. How Does the Calculator Work?

The calculator uses the thermodynamic formula:

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

Where:

\( C_p \) — 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)
\( C_v \) — Heat capacity at constant volume (J/kg·K)

Explanation: This formula relates the heat capacities at constant pressure and constant volume through thermodynamic properties that describe how a substance responds to temperature and pressure changes.

3. Importance of Heat Capacity Calculation

Details: Accurate calculation of heat capacity is essential for thermal system design, energy transfer calculations, chemical process engineering, and understanding material behavior under different thermal conditions.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure temperature is in Kelvin, specific volume in m³/kg, thermal expansion coefficient in 1/K, isothermal compressibility in m²/N, and heat capacities in J/kg·K.

5. Frequently Asked Questions (FAQ)

Q1: Why is Cₚ always greater than Cᵥ for real gases?
A: Because at constant pressure, some energy is used for expansion work against external pressure, requiring more heat input for the same temperature rise.

Q2: What are typical Cₚ values for common gases?
A: Air: ~1005 J/kg·K, Water vapor: ~1996 J/kg·K, Oxygen: ~919 J/kg·K, Nitrogen: ~1040 J/kg·K at room temperature.

Q3: How does temperature affect Cₚ?
A: Cₚ generally increases with temperature as more molecular energy modes become active and contribute to heat capacity.

Q4: What is the relationship between Cₚ and Cᵥ for ideal gases?
A: For ideal gases, Cₚ - Cᵥ = R (gas constant), which is approximately 287 J/kg·K for air.

Q5: When is this formula particularly important?
A: This relationship is crucial when dealing with real gases where ideal gas assumptions break down, especially at high pressures or near critical points.