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 linear molecules based on their atomicity using theoretical principles from statistical mechanics.

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 the molecule)
• \( [R] \) — Universal gas constant (8.314 J/(K·mol))

Explanation: For linear molecules, the formula accounts for translational, rotational, and vibrational degrees of freedom.

3. Importance of C_v Calculation

Details: Understanding C_v is crucial in thermodynamics for predicting how substances absorb heat and how energy is distributed among molecular motions.

4. Using the Calculator

Tips: Simply enter the atomicity (number of atoms in the linear molecule) and click calculate. The atomicity must be a whole number ≥ 1.

5. Frequently Asked Questions (FAQ)

Q1: What is atomicity?
A: Atomicity is the total number of atoms present in a molecule (e.g., 2 for O₂, 3 for CO₂).

Q2: Why is the formula different for linear molecules?
A: Linear molecules have different rotational degrees of freedom (2) compared to nonlinear molecules (3), affecting their heat capacity.

Q3: What's the physical meaning of the 2.5 in the formula?
A: It accounts for the 3 translational and 2 rotational degrees of freedom (3 + 2 = 5), each contributing R/2 to the heat capacity.

Q4: Does this include vibrational contributions?
A: This simple model doesn't include vibrational contributions which become significant at higher temperatures.

Q5: What are typical C_v values for common gases?
A: For diatomic gases (N=2) at room temperature, C_v ≈ 20.8 J/(K·mol); for CO₂ (N=3), C_v ≈ 28.5 J/(K·mol).