Heat Capacity of Real Gases Analysis with Excel

Heat capacity is a measure of how much the energy of a gas changes when its temperature changes. It depends on whether the gas is kept at constant volume or constant pressure. For ideal gases, heat capacity is constant and does not depend on temperature or volume. For real gases, heat capacity is not constant and depends on both temperature and volume.

Real gases are gases that do not follow the ideal gas law exactly, because their molecules have size and interact with each other. These effects become more significant when the gas is compressed, cooled, or near its condensation point. To describe the behavior of real gases, we need more complex equations than the ideal gas law, such as the van der Waals equation or the Redlich-Kwong equation.

The heat capacity of real gases is affected by the molecular structure and the intermolecular forces of the gas. For polyatomic gases, the heat capacity increases as the temperature increases, because the molecules can rotate and vibrate more. For gases with strong intermolecular forces, the heat capacity decreases as the volume decreases, because the molecules are closer together and have less freedom to move. There are also some empirical formulas that can be used to estimate the heat capacity of real gases as a function of temperature and volume.

Basic Theory

The heat capacity of a substance is the amount of heat energy required to raise its temperature by a certain
amount. For real gases, the heat capacity is a function of temperature and pressure. The molar heat capacity at
constant volume (Cv) and constant pressure (Cp) are fundamental thermodynamic properties.

For an ideal gas, Cp and Cv are constant and independent of temperature and pressure. However, real gases deviate
from ideal behavior, and their heat capacities become functions of temperature. The heat capacity relationships for
real gases are often described using empirical equations, such as the Shomate equation.

Procedures for Excel Calculation

Step 1: Gather Data

1. Collect thermodynamic data for the gas of interest, including coefficients for the Shomate equation.

Step 2: Implement Shomate Equation in Excel

1. Enter the temperature values into column A.
2. Use the Shomate equation to calculate Cp for each temperature.

   

Step 3: Create a Table

1. Organize the data in an Excel table with columns for temperature and calculated Cp.

Step 4: Visualization

1. Create a line graph to visualize the variation of Cp with temperature.

Scenario: Calculation for Nitrogen Gas

Let’s consider nitrogen gas (N₂) as an example. The Shomate equation coefficients for nitrogen are as
follows:

Excel Calculation

1. Enter temperatures (in Kelvin) in column A.
2. In cell B2, input the formula for Cp using the Shomate equation.

   

3. Drag the formula down to calculate Cp for different temperatures.
4. Create a table and a line graph to visualize the results.

MATLAB Comparison

1. Use MATLAB to implement the same Shomate equation with the given coefficients.
2. Plot the Cp values against temperature using MATLAB.
3. Compare the Excel and MATLAB results for accuracy.

Excel Table and Result

Result: The table and graph illustrate the variation of Cp with temperature for nitrogen gas based on
the Shomate equation.