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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 linear molecules based on their atomicity using theoretical principles from statistical mechanics.
The calculator uses the formula:
Where:
Explanation: For linear molecules, the formula accounts for translational, rotational, and vibrational degrees of freedom.
Details: Understanding Cv is crucial in thermodynamics for predicting how substances absorb heat and how energy is distributed among molecular motions.
Tips: Simply enter the atomicity (number of atoms in the linear molecule) and click calculate. The atomicity must be a whole number ≥ 1.
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 Cv values for common gases?
A: For diatomic gases (N=2) at room temperature, Cv ≈ 20.8 J/(K·mol); for CO2 (N=3), Cv ≈ 28.5 J/(K·mol).