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Ratio of Molar Heat Capacity given Molar Heat Capacity at Constant Pressure Calculator

Formula Used:

\[ \gamma = \frac{C_p}{C_p - R} \]

J/(K·mol)

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1. What is Ratio of Molar Heat Capacity?

Definition: The ratio of molar heat capacity (γ) is the ratio of the specific heat of the gas at a constant pressure to its specific heat at a constant volume.

Purpose: This ratio is important in thermodynamics for understanding adiabatic processes and the behavior of ideal gases.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma = \frac{C_p}{C_p - R} \]

Where:

Explanation: The formula relates the heat capacity at constant pressure to the heat capacity difference between constant pressure and constant volume.

3. Importance of the Ratio of Molar Heat Capacity

Details: This ratio is crucial for calculating the speed of sound in gases, understanding adiabatic processes, and analyzing thermodynamic cycles.

4. Using the Calculator

Tips: Enter the molar specific heat capacity at constant pressure in J/(K·mol). The value must be greater than the universal gas constant (8.314 J/(K·mol)).

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of γ?
A: γ determines how much a gas will heat up when compressed adiabatically and is important in many thermodynamic processes.

Q2: What are typical values of γ for common gases?
A: For monatomic gases (like He, Ne), γ ≈ 1.67; for diatomic gases (like N2, O2), γ ≈ 1.4.

Q3: Why must Cp be greater than R?
A: Thermodynamically, Cp is always greater than Cv by exactly R, so Cp must be greater than R.

Q4: How is this related to the adiabatic index?
A: The ratio of molar heat capacity (γ) is exactly the same as the adiabatic index used in adiabatic process equations.

Q5: Can this be used for real gases?
A: The formula is exact for ideal gases and a good approximation for real gases at moderate conditions.

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