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:

Where:

• \( \gamma \) — Ratio of molar heat capacity (dimensionless)
• \( C_p \) — Molar specific heat capacity at constant pressure (J/(K·mol))
• \( C_v \) — Molar specific heat capacity at constant volume (J/(K·mol))

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.