Molar Heat Capacity at Constant Pressure given Thermal Pressure Coefficient Calculator

Formula Used:

\[ C_p = \frac{(\Lambda^2) \cdot T}{\left(\frac{1}{K_S} - \frac{1}{K_T}\right) \cdot \rho} + [R] \]

Thermal Pressure Coefficient (Λ):

Pa/K

Temperature (T):

Isentropic Compressibility (K_S):

m²/N

Isothermal Compressibility (K_T):

m²/N

Density (ρ):

kg/m³

Molar Specific Heat Capacity at Constant Pressure (C_p):

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1. What is Molar Specific Heat Capacity at Constant Pressure?

Molar Specific Heat Capacity at Constant Pressure (C_p) of a gas is the amount of heat required to raise the temperature of 1 mole of the gas by 1 °C at constant pressure. It is an important thermodynamic property that characterizes how a substance responds to heat input while maintaining constant pressure.

2. How Does the Calculator Work?

The calculator uses the thermodynamic formula:

\[ C_p = \frac{(\Lambda^2) \cdot T}{\left(\frac{1}{K_S} - \frac{1}{K_T}\right) \cdot \rho} + [R] \]

Where:

\( C_p \) — Molar Specific Heat Capacity at Constant Pressure (J/K·mol)
\( \Lambda \) — Thermal Pressure Coefficient (Pa/K)
\( T \) — Temperature (K)
\( K_S \) — Isentropic Compressibility (m²/N)
\( K_T \) — Isothermal Compressibility (m²/N)
\( \rho \) — Density (kg/m³)
\( [R] \) — Universal Gas Constant (8.314 J/K·mol)

Explanation: This formula relates the heat capacity at constant pressure to various thermodynamic properties including compressibility coefficients, thermal pressure coefficient, and density.

3. Importance of Molar Heat Capacity Calculation

Details: Accurate calculation of molar heat capacity is crucial for understanding thermodynamic processes, designing heat transfer systems, and predicting the behavior of gases under different conditions. It is essential in fields such as chemical engineering, materials science, and atmospheric physics.

4. Using the Calculator

Tips: Enter all values in the specified units. Ensure that Thermal Pressure Coefficient, Temperature, Isentropic Compressibility, Isothermal Compressibility, and Density are all positive values. The calculator will compute the Molar Specific Heat Capacity at Constant Pressure in J/K·mol.

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, where R is the gas constant.

Q2: What are typical values for C_p?
A: For monatomic ideal gases, C_p = 5R/2 ≈ 20.8 J/K·mol. For diatomic gases at room temperature, C_p = 7R/2 ≈ 29.1 J/K·mol.

Q3: How does temperature affect C_p?
A: For ideal gases, C_p is constant with temperature. For real gases, C_p generally increases with temperature due to vibrational modes becoming active.

Q4: What are the units of the thermal pressure coefficient?
A: The thermal pressure coefficient (Λ) has units of Pascal per Kelvin (Pa/K), representing the pressure change per degree temperature change at constant volume.

Q5: When is this formula particularly useful?
A: This formula is especially valuable when working with experimental data where compressibility measurements are available, allowing calculation of heat capacity without direct calorimetric measurements.