Molar Heat Capacity at Constant Volume

📊 intermediate

$$C_v = \frac{f}{2}R$$

The amount of heat required to raise the temperature of one mole of gas by one degree at constant volume.

Variables & Units

$f$

Degrees of freedom

Unit: Integer ($3, 5, 6$)

$R$

Gas constant

Unit: $8.314 J/mol \cdot K$

Key Information

📐 Derived From

Law of Equipartition of Energy.

💡 Example

For a monatomic gas like Helium, $f=3$, so $C_v = 1.5R$.

🔧 Applications

Engine design and thermal modeling.

⚠️ Constraints

Ideal gas; classical limit (no vibrational modes at low T).

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