1. What is Molar Heat Capacity at Constant Volume?

Definition: Molar Specific Heat Capacity at Constant Volume (C_v) 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 C_v 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:

Where:

• \( C_v \) — Molar heat capacity at constant volume (J/(K·mol))
• \( N \) — Atomicity (number of atoms in molecule, ≥3 for non-linear)
• \( [R] \) — Universal gas constant (8.314 J/(K·mol))

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 C_v Calculation

Details: Understanding C_v 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 C_v 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 C_v and C_p?
A: C_v is at constant volume, while C_p (constant pressure) includes work done by expansion and is typically larger.

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

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

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