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The ratio of molar heat capacity (γ) is the ratio of the specific heat of a gas at constant pressure to its specific heat at constant volume. It is also known as the adiabatic index and is an important thermodynamic property of gases.
The calculator uses the formula:
Where:
Explanation: This formula relates the heat capacity ratio to the compressibility properties of a substance under different thermodynamic conditions.
Details: The ratio of molar heat capacity is crucial in thermodynamics for understanding gas behavior, calculating sound speed in gases, and analyzing adiabatic processes. It also plays a key role in various engineering applications including compressor design and fluid dynamics.
Tips: Enter both isothermal compressibility and isentropic compressibility values in m²/N. Both values must be positive numbers greater than zero for accurate calculation.
Q1: What is the typical range for γ values?
A: For monatomic gases, γ is typically around 1.67; for diatomic gases, around 1.4; and for polyatomic gases, values range from 1.1 to 1.33.
Q2: How does temperature affect the heat capacity ratio?
A: The ratio generally decreases with increasing temperature as vibrational modes become excited, increasing the constant volume heat capacity.
Q3: What's the difference between isothermal and isentropic compressibility?
A: Isothermal compressibility measures volume change at constant temperature, while isentropic compressibility measures it at constant entropy (adiabatic and reversible process).
Q4: Can this formula be used for liquids?
A: Yes, the relationship holds for both gases and liquids, though the values and applications differ significantly between the two phases.
Q5: How is this ratio related to the speed of sound?
A: The speed of sound in an ideal gas is given by \( c = \sqrt{\gamma RT/M} \), where R is the gas constant, T is temperature, and M is molar mass.