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| What are adiabatic conditions? |
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An adiabatic change occurs without heat exchange between the system and surroundings. Formally, we can write this as q = 0. We could say that an adiabatic condition is one in which the system is "insulated" from the surroundings. However, in practice even when the system is not well insulated we can also effect an adiabatic change by a very rapid or sudden change in conditions. If the change occurs so rapidly that no heat can be transferred (there is simply no time for the heat to transfer) then the change is effectively adiabatic. So on one extreme we have the insulated system such as the tea thermos shown in the figure. In your laboratory experiment we will use the other approach of a very quick change. Despite the fact that the apparatus you will use is not well insulated you effect an adiabatic change by rapidly pulling down on a level handle that will decrease the volume of the system in a few milliseconds.
Laboratory protocol
You will use a commercial instrument for inducing a volume change. The change in volume is read out as a voltage change, which is converted into digital form in an analog-to-digital converter (ADC), which is connected to the laboratory PC by an interface and registered by the software for the device.
Analysis
The analysis of the data involves linearization of the data followed by regression to determine the slope. The slope is equal to gamma, which is the quantity of interest for calculating the heat capacity.
The propagation of error involves several steps. There are several possible, correct, ways to do the analysis. The document below gives a few points of view on how to calculate propagation of error.
We assume that the gases in this experiment are ideal gases in the derivation. Is this a good assumption? This may be a subject for disucssion. How much more complicated would the analysis be if the gases were non-ideal? The propagation of error is also to be considered in the analysis. While the error in the volume is relatively easy to obtain from the measurement you made of voltage vs. volume the connection of the remaining sources of experimental error to gamma requires further consideration.
Error analysis
The measurement of heat capcity by adiabatic compression provides an excellent example of both random and systematic error. An important part of your report should consist of a discussion of the magnitudes of the various contributions to the error. The systematic error, in this case has several potential origins discussed in the document below. You do not need to write about each of them, but you should consider them carefully and decide which is most likely to account for the discrepancies you observe in your data. The trend in heat capacity is clearly correct and the method could be made more robust. Do a literature search and see if you can find information on this subject.
History
Studies of adiabatic processes have been used for more than 150 years to learn about the heat capacity of gases. Two important methods are the method of Clement and Desormes and the method of Ruchardt. Numerous academic papers have been written even in recent years describing the applications of these methods, which are different from this lab and complement it. Measurement of gamma is important for a number of other applications including an understanding of the speed of sound. Indeed, heat capacity is an important quantity in a number of physical phenomena including, meterology, aeronautical engineering and climate science to name a few. One great source for publications that can complement the information we have presented is in articles in the Journal of Chemical Education. You will also find numerous other adiabatic experiments using the above-named methods at a variety of universities. These may help you to think of topical information to write in your laboratory report.
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