Research Report: Heat Capacity Ratios for Gases

Abstract

The values for heat capacity ratio and the molar heat capacity for this experiment at a constant temperature were obtained using the kundt tube. The values for CO2, N2 and AR recorded here display the figures obtained from the lab procedures for expansion method and the speed of sound method. The ratio of heat capacity at constant pressure to heat capacity at constant volume for the three gases: Nitrogen, Carbon dioxide and Argon were estimated as 1.41(2), 1.29(2), and 1.673(5) by measurement of the speed of sound through the gas. Although the expected possible error for this experiment was a little higher than expected, the values were not far from the expected values basing the equipartion theorem. The values for C, calculated from y, were consistent with the documented literature for carbon (iv) oxide, nitrogen and argon.

The aim of the experiment is:

To Obtain the heat capacity ratio CP/CV using the Sound Velocity method though the use of a Kundt’s tube for the gases Nitrogen, argon dioxide and Argon. The results in this experiment were interpreted basing on the contribution several s degrees of freedom in the molecule of gases to the heat capacity of the compound.

Introduction

In this experiment, heat capacity was determined by both expansion method and the speed of sound method. Pressure measurements in the adiabatic expansion method were obtained using the standard butyl manometer. The expansion method uses the clement and desormes method to determine the cp/cv ratio for gases. The reliability of this experiment is good with a confidence level of up to 95%. For an ideal gas, CP = CV +R, whereby the values of CP and CV represent the molar heat capacities at constant pressure and volume. The speed of sound method for determining heat capacity uses the translational and rotational vibrational potential and kinetic energy of the gases on their speed. The effect is measured on a plane longitudinal sound wave that is propagated in a closed cylindrical tube also known as the kundt’s tube. The physical measurements obtained from these energies for particular species of gases are the molar heat capacities measured at constant pressure and volume. The derivation of the first formula given in this experiment, as documented in this report can be obtained from the shoemaker garland & garland.

For an ideal gas tγ, = Cp/Cv of a gas can also be given as

γ=Mc2/RT (1)

and for Van-del-waal gases,

γ=c2M/RT(1-2a/PV2+2b/V) (2)

thus for or a theoretical value of Cv,

γ=1+R/Cv*(1+2ap/(RT)2) (3)

therefore using the equipartition theorem, the ratio can be given as:

γ=Cp/Cv=1+R/Cv (4)

In electromagnetic waves moving through a vacuum, this expression becomes:

ƒ = c/

using the ideal gas, the heat capacity at constant volume is obtained from formula:

CV= (degrees of freedom/2 )*R (6)

Experimental

The procedures for this experiment, as documented in the lab experiment procedures was followed. The ambient temperature for this experiment was 22.1 C while the ambient pressure was taken to be 752.0mmHg. Since the gas flow rate was low, the pressure of the gas in the tube maybe taken as the same to the ambient pressure. Successive location of the nodes when the screen of the oscilloscope showed a diagonal line was made possible by monitoring the input signal versus the output signal. Reading in the expansion experiment was based on shoemaker and nibler guideline, (p649-652). The values of half wavelength were recorded together with the temperature at the start and end of each series and the respective barometric pressures. A value of 1.004 was used for carbon dioxide and nitrogen while that of 2.004 kHz was used for argon as the frequency of the generated input sound wave.

The values for half wavelength were averaged and the obtained mean used to calculate the speed of sound for every gas. The ratio of heat capacities was calculated using the value of speed using the formula given above. / The values of CV were also calculated to verify the document literature values. The periods for the generated sound was measured by the oscilloscope and converted to frequency using the equation=i/p. This conversation was done immediately after data collection. The speed of sound was obtained from the measurement of respective half wavelength using the relationship c=2(half wavelength) x frequency. the heat capacity ration was also defined using the formula, wavelength = cvb/cp. the gases used were simple, pure, monoatomic and diatomic gases, thus their heat capacity can be obtained using the ideal gas equation and treating the gases as van der waal gases ‘due to large errors found in the results in this experiment, a meaningful conclusion needs a critical analysis of data. The consistency low values that were obtained in the experiment indicated that there were some systematic errors that occurred in the experiment. A comparison of obtain speeds compared to documented speeds showed some deviation. Error analysis on the results was done and the possible error in the measured wavelength. This was done as outlined in garland et al p 38. Due to the large in the wavelength and effect in propagation through the calculation of speed and heat capacity, the calculated results for heat capacity could not be taken entirely as valid. There would be need to reduce the error in the wavelength by 3 orders of magnitude for the data to be valid. However the results agree with the predicted and documented values. A primary cause of the errors could be the instability in reading the oscilloscope. There were some fluctuations in the amplitude of the signal which made determinations of the amplitude difficult. This cause, however, could not be readily determined. The treatment of the gases as van der Waal gases, on the other hand, only led to minor changes in the result. This was expected due to the condition used in the gases.

The experiment procedure was not enough to determine whether the gases were linear or nonlinear. The average speed of molecules in gases, are equal to the average velocities of molecules in any direction. This is because speed is simply the measure of magnitude of velocity for each molecules of gas. Velocity of a gas is the speed of gas in a certain direction, thus the average speed in a particular direction.

Since sound is transmitted through the motion of molecules, the rate through which sound travels in gases is the same as the speed of molecules of gases since the speed of molecules is not a function of the gases pressure, but the temperature, the speed of sound in gases does not depend on pressure at all.

Conclusion

As noted earlier there is good agreement of the figures calculated with those of predicted. Though there are some errors in the experiment. Since the error is relatively large, it would not be easy to draw a difference between the linear and nonlinear structures of the polyatomic molecules of gases such as that of carbon dioxide. Also, since the difference in the equipartition, theorem of gases and the effect of wavelengths are in the order of -1, the errors need to be reduced.

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