Molar Heat Capacity at Constant Volume given Compressibility Calculator

Formula:

\[ C_v = \frac{K_S}{K_T} \times C_p \]

Isentropic Compressibility (K_S):

m²/N

Isothermal Compressibility (K_T):

m²/N

Molar Specific Heat Capacity at Constant Pressure (C_p):

J/(K·mol)

Molar Specific Heat Capacity at Constant Volume (C_v):

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1. What is Molar Heat Capacity at Constant Volume?

Molar Specific Heat Capacity at Constant Volume (C_v) is the amount of heat required to raise the temperature of 1 mole of a substance by 1 degree Celsius at constant volume. It is an important thermodynamic property that characterizes how a substance responds to heat input when its volume is fixed.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_v = \frac{K_S}{K_T} \times C_p \]

Where:

\( C_v \) — Molar Specific Heat Capacity at Constant Volume (J/(K·mol))
\( K_S \) — Isentropic Compressibility (m²/N)
\( K_T \) — Isothermal Compressibility (m²/N)
\( C_p \) — Molar Specific Heat Capacity at Constant Pressure (J/(K·mol))

Explanation: This formula relates the heat capacities at constant volume and constant pressure through the ratio of isentropic to isothermal compressibility, providing a fundamental thermodynamic relationship.

3. Importance of C_v Calculation

Details: Accurate calculation of molar specific heat capacity at constant volume is crucial for understanding thermodynamic processes, designing heat transfer systems, and studying material properties in various engineering and scientific applications.

4. Using the Calculator

Tips: Enter isentropic compressibility and isothermal compressibility in m²/N, and molar specific heat capacity at constant pressure in J/(K·mol). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: What are typical values for C_v?
A: For monatomic ideal gases, C_v = 3/2R; for diatomic gases, C_v = 5/2R; and for polyatomic gases, C_v values are higher and more complex.

Q3: How are compressibility ratios related to heat capacities?
A: The ratio K_S/K_T equals C_v/C_p, which is the reciprocal of the adiabatic index (γ) for ideal gases.

Q4: When is this formula particularly useful?
A: This relationship is especially valuable when direct measurement of C_v is difficult, but compressibility measurements are available.

Q5: Are there limitations to this equation?
A: This formula is generally valid for ideal gases and many real gases under moderate conditions, but may require modifications for complex systems or extreme conditions.