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:

Where:

• \( γ \) — Ratio of molar heat capacity (dimensionless)
• \( C_v \) — Molar specific heat capacity at constant volume (J/(K·mol))
• \( R \) — Universal gas constant (8.314 J/(K·mol))

Explanation: The formula shows how the heat capacity ratio depends on the constant-volume heat capacity and the universal gas constant.

3. Importance of Heat Capacity Ratio

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 volume (Cv) in J/(K·mol). The value must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of γ?
A: γ determines how much a gas heats up when compressed and how much work it can do during expansion.

Q2: What are typical values of γ?
A: For monatomic gases γ ≈ 1.67, for diatomic gases γ ≈ 1.4, and for polyatomic gases γ is typically between 1.1 and 1.33.

Q3: Why does R appear in the formula?
A: R represents the difference between constant-pressure and constant-volume heat capacities (Cp - Cv = R for ideal gases).

Q4: How is γ related to degrees of freedom?
A: γ = 1 + 2/f where f is the number of degrees of freedom of the gas molecules.

Q5: Can γ be less than 1?
A: No, since Cp > Cv for all gases, γ is always greater than 1.