Heat Capacity Visualizer
Heat Capacity Visualizer plots heat capacity vs. temperature for gases or solids using material properties and temperature range.
Formulas Used in Heat Capacity Visualizer
The visualizer computes the molar heat capacity (\\(C_v\\) or \\(C_p\\)) as a function of temperature:
Monatomic Gas:
\\[ C_v = \frac{3}{2} R, \quad C_p = C_v + R \\]Diatomic Gas:
\\[ C_v = \frac{5}{2} R, \quad C_p = C_v + R \\]Solid/Liquid:
\\[ C_p = a + b T + c T^2 \\]Where:
- \\(C_v\\): Molar heat capacity at constant volume (J/(mol·K))
- \\(C_p\\): Molar heat capacity at constant pressure (J/(mol·K))
- \\(T\\): Temperature (K)
- \\(R\\): Gas constant (\\(8.314462618 \, \text{J/(mol·K)}\\))
- \\(a\\): Constant coefficient (J/(mol·K))
- \\(b\\): Linear coefficient (J/(mol·K²))
- \\(c\\): Quadratic coefficient (J/(mol·K³))
Example Calculations
Example 1: Monatomic Gas, \\(C_v\\), \\(T = 300 \, \text{K}\\)
\\[
R = 8.314462618 \, \text{J/(mol·K)}
\\]
\\[
C_v = \frac{3}{2} R = \frac{3}{2} \cdot 8.314462618 \approx 12.4717 \, \text{J/(mol·K)}
\\]
Example 2: Solid, \\(C_p = 25 + 0.01 T\\), \\(T = 300 \, \text{K}\\)
\\[
C_p = 25 + 0.01 \cdot 300 = 25 + 3 = 28 \, \text{J/(mol·K)}
\\]
Result: \\(C_v \approx 12.4717 \, \text{J/(mol·K)}\\) for monatomic gas; \\(C_p \approx 28 \, \text{J/(mol·K)}\\) for solid.