# The Heat Capacity Ratio of Gases

## The Heat Capacity Ratio of Gases

• Submitted By: dyoyo
• Date Submitted: 02/04/2014 5:20 PM
• Category: Science
• Words: 1015
• Page: 5
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Purpose: The purpose of this experiment was to determine the heat capacity ratio (γ) for Helium (He), Nitrogen (N) and Carbon dioxide (CO2) and then compares these values with the theoretical (literature) values.
Introduction:
Heat capacity is an important thermodynamic concept that is related to both entropy and enthalpy. Heat capacity (C) is a path function that is defined as the amount of heat required to change a substance's temperature by a given amount. Heat capacity can be calculated suing the following formula:
C= q∆T
Since heat capacity is a path function, it has to thermodynamic paths: heat capacity at constant volume (Cv) and heat capacity at constant pressure (Cp). The two heat capacities can be expressed in the following equation:
γ= CpCv
And Cp=Cv+nR
And CpCv=In p1-In p2In p1-In p3
The is an association between the heat capacity (C) and constant volume (Cv) and the shape and number of atoms in the gas:
Table 1: The effect of the mono, di- and triatomic gases on the heat capacity at constant volume (Cv).
Class | Gas | Cv (J/K.mol) |
Monoatomic | H, He, Ar | 12.5 (=3/2R) |
Diatomic | N2,Cl2, F2 | 20.8 (=5/2R) |
Linear triatomic | CO2, NO2, H2O(g) | 29 (=7/2R) |

Molecules undergo translation, vibration and rotation. Understanding these three types of movements can explain the association between the heat capacities. Translational energy= 3/2 RT and Rotational energy= RT (linear molecules) or 3/2 RT (non- linear molecules) and vibrational energy= (3N-5) RT (linear molecules) or (N-2) RT (non-linear molecules).

Data:
Pressure of Chemicals
Table2: The initial and final pressure in helium (He), nitrogen (N2) and carbon dioxide (CO2).
Helium (He) (mm Hg) | Carbon dioxide (CO2)(mm Hg) | Nitrogen (N2)(mm Hg) |
p1 (±0.4) | p3 (±0.4) | p1 (±0.4) | p3 (±0.4) | p1 (±0.4) | p3 (±0.4) |
220.4 | 29.1 | 261.8 | 45.8 | 278.7 |...