# EXPERIMENT 1

EXPERIMENT 1: THE HEAT CAPACITY RATIO

FRANK KAYEYE

100886802

Purpose:

The purpose of this experiment was to calculate the heat capacity ratio γ for three gases find in three different classes. The three different gases and their classes are; helium which is classified as a monatomic gas, nitrogen which is classified as a diatomic gas and carbon dioxide, which is classified as a linear triatomic gas. After these experimental heat capacities ratio were calculated they were then compared with theoretical values.

Introduction:

Heat capacity is a very important concept in thermodynamics. It is directly used to calculate the entropies and enthalpies of a system. Kirchhoff ‘s law is used to find the change in heat of a reaction with respect to temperature if the heat capacities are known, and the entropies of substance can be calculated from heat capacity and temperature data. The heat capacity of a substance of system is the amount of energy required to raise its temperature by one degree kelvin. It is determined by heating a substance and measuring the amount of heat absorbed and the resulting rise in temperature. C=q/ΔT

In thermodynamics, heat capacity can be described as a path function. It can have any value. The two convenient thermodynamic paths are the constant volume (Cv), and the constant heat capacity (Cp), which have different values. The equation that relate these two heat capacities in a ideal gas is:

Cp= Cv+nR

The three different gas classes have different heat capacities. This is because molecules absorb heat differently, since there is three type of movements in molecules; translation, vibration, and rotation. When gases are heated, energy is absorbed in these modes and molecules, translate, vibrate and rotate faster, hence the temperature increases. Thus the predicted heat capacities for the three classes of gas will be; for monatomic Cv= 3R/2 = 12J/mol. K, for diatomic Cv=7R/2=29.1J/mol. K, and for linear polyatomic Cv=13R/2=54.0J/mol. K. In this experiment the ratio Cp/Cv = γ was calculated. However Cv was calculated using the equation Cp= Cv+nR. Since this experiment was conducted in an adiabatic system, which is a system that no heat can enter or escape. Insulating the system or performing the process quickly enough that heat does not have time to escape. For an adiabatic system dq= 0. According to the first law of thermodynamic; dU=-PdV, when using the equation that are true for any ideal gas; dU= CvdT . When combining the two equations together one obtains; - dV/V=Cv/nR. dT/T. When integrating from one thermodynamic state to the other it gives; -ln (V2/V1)=Cv/nR (T2/T1). Since this an adiabatic expression where V2 is greater than V1, the gas has to cool so that T2 becomes less than T1. When using the two state ideal gas relationship of; T2/T1=P2V2/P1V1, the expression equation gives ln (P2/P1)=-Cp/Cv ln (V2/V1). Since P1, V1 and T1 is the same as P2, V2, T2, therefore P1V1/V1=P2V2/T2. Therefore for one mole of ideal gas; P2/P3=P2V2/P1V1 or V2/V1=P1/P3. The equation becomes:

Cp/Cv=lnP1-lnP2/lnP1-lnP3=γ

The vibration movement can have a huge impact on Cv. For quantum mechanics it is known that the energy gap between vibration levels depends on the vibration frequency; E= hv. In most cases this gap is too large to be thermally excited, and the contribution to Cv is very small, the gap between every levels is small and there is a significant contribution to Cv. The vibration contribution of nitrogen is negligible because the vibration is too large. The linear plyatomic...

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