1. What is Specific Heat Ratio?

Definition: The specific heat ratio (γ) is the ratio of specific heat at constant pressure (c_p) to specific heat at constant volume (c_v).

Purpose: This dimensionless quantity is important in thermodynamics, particularly in analyzing isentropic processes and compressible flows.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \gamma \) — Specific heat ratio (dimensionless)
• \( c_p \) — Specific heat at constant pressure (J/kg·K)
• \( c_v \) — Specific heat at constant volume (J/kg·K)

Explanation: The ratio compares how much more energy is required to raise temperature at constant pressure versus constant volume.

3. Importance of Specific Heat Ratio

Details: This ratio is crucial in thermodynamics for:

• Analyzing ideal gas processes
• Designing nozzles and diffusers
• Calculating speed of sound in gases
• Understanding isentropic flow relationships

4. Using the Calculator

Tips: Enter both specific heat values in J/kg·K. Both must be positive numbers. For ideal gases, c_p is always greater than c_v.

5. Frequently Asked Questions (FAQ)

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

Q2: Why is c_p always greater than c_v?
A: At constant pressure, energy is needed for both temperature increase and expansion work, while at constant volume all energy goes to temperature change.

Q3: How does γ vary with temperature?
A: γ decreases slightly with increasing temperature as vibrational modes become active in molecules.

Q4: What's the relationship between γ and degrees of freedom?
A: γ = 1 + 2/f where f is degrees of freedom (f=3 for monatomic, 5 for diatomic at moderate temps).

Q5: Where is γ used in engineering?
A: In nozzle design, turbine analysis, shock wave calculations, and thermodynamic cycle analysis.