AbstractAn ideal gas is one which obeys the equation of state i.e. PV=nRT. A Pasco Adiabatic apparatus was used to measure specific voltages for P, V & T which were converted using conversion formulas. The logarithms of the resulting values were found and graphed against each other and from these graphs the heat capacities of the four different gases were found.IntroductionHeat capacity or thermal capacity is a measurable physical quantity equal to the ratio of the heat added to (or removed from) an object to the resulting temperature change.
This experimental procedure uses a Pasco Adiabatic apparatus to determine the heat capacity for four different gases, air, Nitrogen, Argon and Carbon Dioxide. TheoryAn ideal gas is one which obeys the equation of state i.e. ? =? where:n =the number of moles R = 8.314 J K-1mol-1, the universal gas constant,P=the gas pressure, V =the volume of the gas, T =the temperature of the gas (in Kelvin).At the pressures and temperatures used in this experiment the gases used can be considered to behave closely to that of ideal gases .
The thermodynamic principle of adiabatic compression was also utilised in this experiment. An adiabatic process is one in which no heat is gained or lost by the system. The first law of thermodynamics with Q=0 shows that all the change in internal energy is in the form of work done . For an adiabatic process (Q=0) of an ideal gas : PV’ = Constant and ’ = CP/CV (CP,CV = molar heat capacity at constant pressure/volume). Combining the ideal gas law and the above equations: In order to calculate ’ the logs of the above equations are used: And therefore, A plot of log(P) against log(V) should be a straight line with slope €’? and a plot of log(T) against log(V) should be a straight line with slope €’(?€’1). MethodThe first step was to switch on the PC and the interface unit on the adiabatic apparatus. On the computer, the science workshop software was opened and the three input channels were established as voltage sensors. Before analysing any of the gases, the chamber of the Pasco Adiabatic apparatus had to be flushed to ensure accurate results. Following this, the apparatus was used to derive a conversion formula for the volume voltage values using the known dimensions in the apparatus. To do this, the base of the piston was positioned at 15 cm and the gas was compressed until the base of the piston reached 8cm. Also, as soon as the piston began to be pressed, the record button was pressed and then stopped when the piston base was at 8 cm. The diameter of the gas cylinder was given to be 4.448 cm. With the voltage readings obtained through the recording, they were saved in an excel spreadsheet. Only the voltage readings from channel A were used for finding a volume formula. Once this was done, the voltage readings were taken for each gas. The four gases in question were Air, Argon, Nitrogen and Carbon Dioxide. For each case, the gas was pumped from the canisters into the gas cylinder by a lab technician. As soon as the gas was in place, the piston was pressed from 15 cm to 8 cm and the voltage readings were captured by the software. From there, the voltages for the three channels were entered in an excel spreadsheet. The relevant conversions into volume, pressure and temperature were calculated. Subsequently, the log of each property was found and two graphs were formed, log(P) vs log(V) and log(T) vs log(V). The experimental values of ’ were then found from the slopes.Results Figure 1: A graph of log(P) against log(V) for air Figure 2: A graph of log(T) against log(V) for air Figure 3: A graph of log(P) against log(V) for CO2 Figure 4: A graph of log(T) against log(V) for CO2 Figure 5: A graph of log(P) against log(V) for Argon Figure 6: A graph of log(T) against log(V) for Argon Figure 7: A graph of log(P) against log(V) for Nitrogen Figure 8: A graph of log(T) against log(V) for Nitrogen DiscussionThe voltage readings taken from the software were put through conversion formulas and then the log of each was found so they correct information could be graphed. For air, the two graphs procured contained data points which followed the expected trend. This showcased the linear relationship between log(P) and log(V) as well as log(T) and log(V). Air is considered a diatomic gas as it is mostly composed of nitrogen, so the expected value for ’ is 1.4. The experimental result achieved was 2.1913 and 14.054. For nitrogen, the graphs also confirmed the linear relationships between log(P) and log(V) as well as log(T) and log(V). Nitrogen is also a diatomic gas, so the expected value for ’ is 1.4. The results obtained in the lab gave values of 1.9674 and 8.2156. For carbon dioxide, this same straight-line trend was present in both graphs. Carbon dioxide is a triatomic gas, and the expected value for ’ was 1.286. The values gathered in this experiment were 2.1281 and 10.873. Lastly, for argon, a monoatomic gas, the expected value of ’ is 1.667. In the experiment, the values achieved were 1.7645 and 5.8204. It was clear from these results that although most of the values obtained from the log(P) against log(V) graphs were close to the expected ones, the ones obtained from the log(T) against (V) were not. This means that there was an error someone in the experimental procedure.ConclusionOverall, the outcome of this experiment was relatively successful. The ratio of specific heat capacities were obtained for a monoatomic, a diatomic and a triatomic gas using a Pasco adiabatic apparatus and science workshop software. The relevant calculations were performed to convert voltage into volume, pressure and temperature. However, the heat capacity values calculated from the log(T) against log(V) graphs were not in the acceptable range of values meaning that there was an error in the experimental procedure.References 3rd Year Lab Manual. (N/A). Ratio of heat capacities. Available: N/A. Last accessed 03/12/2018. N/A. (N/A). Adiabatic Processes. Available: Last accessed 03/12/2018.