Heat Capacity Ratios for Gases Essay Example

Heat Capacity Ratios for Gases Paper Heat Capacity Ratios for Gases Research Report 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. We will write a custom essay sample on Heat Capacity Ratios for Gases specifically for you for only $16.38 $13.9/page Order now We will write a custom essay sample on Heat Capacity Ratios for Gases specifically for you FOR ONLY $16.38 $13.9/page Hire Writer We will write a custom essay sample on Heat Capacity Ratios for Gases specifically for you FOR ONLY $16.38 $13.9/page Hire Writer 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 deriv ation 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 t?, = Cp/Cv of a gas can also be given as ?=Mc2/RT (1) and for Van-del-waal gases, ?=c2M/RT(1-2a/PV2+2b/V) (2) thus for or a theoretical value of Cv, ?=1+R/Cv*(1+2ap/(RT)2) (3) therefore using the equipartition theorem, the ratio can be given as: ?=Cp/Cv=1+R/Cv (4) In electromagnetic waves moving through a vacuum, this expression becomes: ? = 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 anal ysis 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 determ ined. 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.

Brief History of the US Federal Income Tax

Brief History of the US Federal Income Tax Money raised through income tax is used to pay for the programs, benefits, and services provided by the US government for the benefit of the people. Essential services such as national defense, food safety inspections, and federal benefit programs including Social Security and Medicare could not exist without the money raised by the federal income tax. While the federal income tax did not become permanent until 1913, taxes, in some form, have been a part of American history since our earliest days as a nation. Evolution of Income Tax in America While taxes paid by American colonists to Great Britain were one of the main reasons for the Declaration of Independence and ultimately the Revolutionary War, Americas Founding Fathers knew that our young country would need taxes for essential items such as roads and especially defense. Providing the framework for taxation, they included procedures for the enactment of tax law legislation in the Constitution. Under Article I, Section 7 of the Constitution, all bills dealing with revenue and taxation must originate in the House of Representatives. Otherwise, they follow the same legislative process as other bills. Before the Constitution   Before final ratification of the Constitution in 1788, the federal government lacked the direct power to raise revenue. Under the Articles of Confederation, money to pay the national debt was paid by the states in proportions to their wealth and at their discretion. One of the goals of the Constitutional Convention was to ensure that the federal government had the power to levy taxes. Since Ratification of the Constitution Even after the ratification of the Constitution, most federal government revenues were generated through tariffs taxes on imported products and excise taxes taxes on the sale or use of specific products or transactions. Excise taxes were considered regressive taxes because people with lower incomes had to pay a higher percentage of their income than did people with higher incomes. The most recognized federal excise taxes still in existence today include those added to the sales of motor fuels, tobacco, and alcohol. There are also excise taxes on activities, such as gambling, tanning or the use of highways by commercial trucks.​ As true with the modern income tax, those early taxes were far from popular among the people.But with the spirit of the American Revolution and independence still running high, some of the people took their dislike of taxes to far higher level. Between 1786 and 1799, three organized rebellions- all protesting various taxes- challenged the authority of the state and federal governments to generate needed revenue. Shays Rebellion from 1786 to 1787 was raised by a group of farmers in objection to what they considered the unfair methods used by state and local tax collectors. The Whiskey Rebellion of 1794 in western Pennsylvania came in protest to what President George Washingtons Secretary of the Treasury Alexander Hamilton wrongly considered an innocuous excise tax â€Å"upon spirits distilled within the United States, and for appropriating the same.† Finally, Fries’ Rebellion of 1799 was led by a group of Pennsylvania Dutch farmers opposed to a new federal government tax on houses, land, and slaves. While the farmers owned lots of land and houses, they were far from keen on paying taxes on slaves none of  them owned. Early Income Taxes Came and Went During the Civil War from 1861 to 1865, the government realized that tariffs and excise taxes alone could not generate enough revenue to both run the government and conduct the war against the Confederacy. In 1862, Congress established a limited income tax only on people who made more than $600 but abolished it in 1872 in favor of higher excise taxes on tobacco and alcohol. Congress re-established an income tax in 1894, only to have the Supreme Court declare it unconstitutional in 1895. 16th Amendment Forward In 1913, with the costs of  Ã‚  World War I looming, ratification of the 16th Amendment permanently established the income tax. The 16th  Amendment states: â€Å"The Congress shall have power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several States, and without regard to any census or enumeration.† The 16th Amendment gave Congress the power to tax the incomes of all individuals and the profits of all businesses. The income tax enables the federal government to maintain the military, construct roads and bridges, enforce the laws and federal regulations, and carry out other duties and programs.   By 1918, government revenue generated from the income tax exceeded $1 billion for the first time and topped $5 billion by 1920. The introduction of the mandatory withholding tax on employee wages in 1943 increased tax revenue to almost $45 billion by 1945. In 2010, the IRS collected nearly $1.2 trillion through income tax on individuals and another $226 billion from corporations. The Role of Congress in Taxation According to the US Treasury Department, the goal of Congress in enacting tax-related legislation is to balance the need to raise revenue, the desire to be fair to taxpayers, and the desire to influence the way taxpayers save and spend their money.