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Heat Capacity Ratio Formula:
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The heat capacity ratio (γ), also known as the adiabatic index, is the ratio of specific heat at constant pressure (C_p) to specific heat at constant volume (C_v). It is an important thermodynamic property used in various engineering and physics applications.
The calculator uses the heat capacity ratio formula:
Where:
Explanation: This ratio describes how a substance's internal energy changes with temperature under different conditions and is particularly important in gas dynamics and thermodynamics.
Details: The heat capacity ratio is crucial in calculating the speed of sound in gases, designing nozzles and diffusers, analyzing compression processes, and understanding thermodynamic cycles like the Carnot cycle.
Tips: Enter both specific heat values in J/kg·K. Both values must be positive and non-zero. The result is a dimensionless quantity.
Q1: What are typical values of γ for common gases?
A: For monatomic gases (like helium, argon): γ ≈ 1.67; for diatomic gases (like nitrogen, oxygen): γ ≈ 1.4; for polyatomic gases: γ ≈ 1.33 or lower.
Q2: Why is γ always greater than 1?
A: C_p is always greater than C_v because at constant pressure, some energy is used for expansion work, requiring more heat input for the same temperature change.
Q3: How does γ relate to the degrees of freedom of a molecule?
A: γ = 1 + 2/f, where f is the number of degrees of freedom. This relationship helps explain why different types of gases have different γ values.
Q4: What is the significance of γ in compressible flow?
A: γ appears in many compressible flow equations, including those for Mach number, isentropic flow relations, and shock wave calculations.
Q5: Can γ be less than 1?
A: No, since C_p is always greater than C_v, the ratio γ = C_p/C_v is always greater than 1 for all substances.