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Molar Heat Capacity at Constant Volume of Non-Linear Molecule Calculator

Formula Used:

\[ C_v = ((3 \times N) - 3) \times [R] \]

(≥3 for non-linear)

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1. What is Molar Heat Capacity at Constant Volume?

Definition: Molar Specific Heat Capacity at Constant Volume (Cv) is the amount of heat required to raise the temperature of 1 mole of a substance by 1 Kelvin at constant volume.

Purpose: This calculator determines Cv for non-linear molecules based on their atomicity (number of atoms in the molecule).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ C_v = ((3 \times N) - 3) \times [R] \]

Where:

Explanation: For non-linear molecules, there are 3 translational and 3 rotational degrees of freedom, with the remaining (3N-6) being vibrational. However, at moderate temperatures, vibrational contributions are often negligible, leading to this simplified formula.

3. Importance of Cv Calculation

Details: Understanding Cv is crucial in thermodynamics for calculating energy changes, designing heat transfer systems, and understanding molecular behavior.

4. Using the Calculator

Tips: Enter the atomicity (number of atoms in the molecule). For non-linear molecules, this must be ≥3. The calculator will compute Cv using the universal gas constant.

5. Frequently Asked Questions (FAQ)

Q1: Why is atomicity ≥3 for this calculator?
A: This formula applies specifically to non-linear molecules, which must have at least 3 atoms (e.g., H2O, NH3).

Q2: What's the difference between Cv and Cp?
A: Cv is at constant volume, while Cp (constant pressure) includes work done by expansion and is typically larger.

Q3: How does molecular structure affect Cv?
A: Linear molecules have different degrees of freedom (5 total: 3 translational + 2 rotational), leading to different Cv values.

Q4: What are typical Cv values for common molecules?
A: For non-linear triatomic molecules (N=3), Cv ≈ 25 J/(K·mol); for N=4 (e.g., NH3), ≈ 37 J/(K·mol).

Q5: Does temperature affect Cv?
A: At higher temperatures, vibrational modes become significant, increasing Cv beyond this simple calculation.

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