Molar Heat Capacity at Constant Pressure given Volumetric Coefficient of Thermal Expansion Calculator

Formula Used:

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

Volumetric Coefficient of Thermal Expansion (α):

1/K

Temperature (T):

Isothermal Compressibility (K_T):

m²/N

Isentropic Compressibility (K_S):

m²/N

Density (ρ):

kg/m³

Molar Specific Heat Capacity at Constant Pressure (C_p):

Unit Converter ▲

Unit Converter ▼

From:	To:

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 mol of the gas by 1 °C at constant pressure. It is a fundamental 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 relation:

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

Where:

\( C_p \) — Molar Specific Heat Capacity at Constant Pressure (J/(K·mol))
\( \alpha \) — Volumetric Coefficient of Thermal Expansion (1/K)
\( T \) — Temperature (K)
\( K_T \) — Isothermal Compressibility (m²/N)
\( K_S \) — Isentropic Compressibility (m²/N)
\( \rho \) — Density (kg/m³)

Explanation: This formula relates the heat capacity to measurable thermodynamic properties through fundamental thermodynamic identities.

3. Importance of C_p Calculation

Details: Accurate calculation of C_p is crucial for understanding energy transfer processes, designing thermal systems, predicting phase changes, and analyzing thermodynamic cycles in engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure that isothermal compressibility is greater than isentropic compressibility. All input values must be positive numbers.

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: Why is isothermal compressibility greater than isentropic compressibility?
A: Isentropic compressibility is smaller because during adiabatic processes, temperature changes affect the compressibility, making the substance appear "stiffer."

Q3: What are typical values of C_p for common gases?
A: For monatomic gases (He, Ar): ~20.8 J/(mol·K); for diatomic gases (N₂, O₂): ~29.1 J/(mol·K); values vary with temperature.

Q4: How does temperature affect C_p?
A: C_p generally increases with temperature as more vibrational modes become active in molecules.

Q5: Can this formula be used for all substances?
A: This thermodynamic relation is general and applies to all substances, though the specific values of the parameters vary widely between different materials.