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Specific heats of gases
Intermediate
Cv depends on degrees of freedom.
C_v = (f/2)RC_v = (f/2)R, C_p = C_v + R, γ = 1 + 2/f. Measured values test the number of degrees of freedom.
Monatomic γ = 5/3, diatomic 7/5.
Hydrogen's C_v drops at low T due to quantised rotation.
In more detail
The molar specific heats of gases follow from degrees of freedom: C_v = (f/2)R. For monatomic gases, C_v = 3R/2, and for diatomic gases at room temperature, C_v = 5R/2.
Real-world uses
- Engineers compute energy requirements for heating gases.
- Ratio of specific heats for air is derived from these values.
- Engineers use the heat capacity of air in the design of engines and compressors, which depends on the gas's degrees of freedom.
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Frequently asked questions
What is C_p for an ideal gas?
C_p equals C_v plus R.
Why is the ratio about 1.4 for air?
Because air is mostly diatomic, giving C_p/C_v = 7/5.
Why does the heat capacity of a gas depend on its molecules?
Each degree of freedom absorbs energy, so more complex molecules have higher heat capacities.
Related topics in Kinetic Theory & Statistical Physics
Collision frequency · Degrees of freedom · Equipartition theorem · Maxwell–Boltzmann distribution · Most probable speed · Average, rms and most probable speeds