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Adiabatic Index Formula:
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The Adiabatic Index (k) is the ratio of the heat capacity at constant pressure (Cp) to heat capacity at constant volume (Cv). It is a dimensionless quantity that describes how a gas responds to adiabatic processes.
The calculator uses the Adiabatic Index formula:
Where:
Explanation: The adiabatic index represents the ratio of specific heats and indicates how the internal energy of a gas changes with temperature under constant pressure versus constant volume conditions.
Details: The adiabatic index is crucial in thermodynamics for analyzing compression and expansion processes in gases, calculating sound speed in gases, and studying shock waves and fluid dynamics.
Tips: Enter both heat capacity values in J/kg·K. Both values must be positive and non-zero for accurate calculation.
Q1: What are typical values of adiabatic index for common gases?
A: For monatomic gases (like helium, argon): ~1.67; for diatomic gases (like nitrogen, oxygen): ~1.4; for polyatomic gases: typically between 1.1-1.33.
Q2: How does temperature affect the adiabatic index?
A: The adiabatic index generally decreases with increasing temperature as more vibrational modes become active in polyatomic molecules.
Q3: What is the relationship between adiabatic index and degrees of freedom?
A: \( k = 1 + \frac{2}{f} \), where f is the number of degrees of freedom of the gas molecules.
Q4: Why is adiabatic index important in engineering applications?
A: It's essential for designing compressors, turbines, nozzles, and understanding combustion processes and aerodynamic flows.
Q5: How does the adiabatic index relate to the speed of sound?
A: The speed of sound in an ideal gas is given by \( c = \sqrt{kRT} \), where R is the gas constant and T is temperature.