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Ratio of Molar Heat Capacity Calculator

Ratio of Molar Heat Capacity Formula:

\[ \gamma = \frac{C_p}{C_v} \]

J/(K·mol)
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: It's an important parameter in thermodynamics that helps characterize the behavior of gases under different conditions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \gamma = \frac{C_p}{C_v} \]

Where:

Explanation: The ratio compares how much heat is required to raise the temperature of a gas at constant pressure versus constant volume.

3. Importance of Ratio of Molar Heat Capacity

Details: This ratio is crucial in thermodynamics for calculating adiabatic processes, speed of sound in gases, and understanding the behavior of ideal gases.

4. Using the Calculator

Tips: Enter the molar specific heat capacities at constant pressure (Cp) and constant volume (Cv) in J/(K·mol). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical value for γ?
A: For monatomic ideal gases, γ ≈ 1.67. For diatomic gases at room temperature, γ ≈ 1.4.

Q2: Why is Cp always greater than Cv?
A: At constant pressure, some energy goes into work done by expansion, so more heat is needed compared to constant volume.

Q3: How does γ relate to degrees of freedom?
A: γ = 1 + (2/f) where f is the degrees of freedom of the gas molecules.

Q4: Can γ be less than 1?
A: No, since Cp is always greater than Cv, γ is always greater than 1.

Q5: How is γ used in adiabatic processes?
A: In adiabatic processes, PV^γ = constant, where P is pressure and V is volume.

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