The pressure-temperature relation for liquid-vapour phase equilibrium of water substance
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DEN107 Thermodynamics - Laboratory The pressure-temperature relation for liquid-vapour phase equilibrium of water substance Paul James Ashley 05 003984 3 April 23rd 2006 Abstract The objective of the experiment is to verify that the relationship between pressure and temperature is described by the Clausius-Clapeyron equation, derived in two forms in the theory. Two experiments were carried out on two sets of equipment, one for pressures below atmospheric and one for those above atmospheric. The results are presented, and graphs show that there is an almost exact linear trend for pressures above atmospheric, and an approximately linear relationship for pressures below atmospheric. Calculations with comparison to published tables show that the results from this experiment do indeed follow the trend described by the Clausius-Clapeyron, and as such the objectives were met. Where any differences exist, these are accounted for by experimental and human error, of which experimental error was estimated from the graphs at 4.6%. Contents Introduction page 3 Background Theory page 4 Apparatus page 6 Experimental Procedure page 7 Results page 8 Discussion page 10 Conclusions page 13 References page 14 Introduction The experiment performed in the laboratory was to investigate the relationship between pressure and temperature for two phases of water in equilibrium. Before the experiment was performed it was assumed that the two variables are related, and this assumption is supported by the derivation of the Clausius-Clapeyron Equation in the background theory.
4 (Pressures recorded in mmHg were converted to kPa by multiplying by 0.1333, and temperatures recorded on the Celsius scale were converted to Kelvin by adding 273.2 K) Atmospheric Conditions Ambient Temperature 21.5 oC 294.7 K Atmospheric Pressure 751.55 mmHg 100.18 kPa Fig. 5 These results are displayed on the figures below. Fig. 6 Fig. 7 Discussion While the observations were being recorded it quickly became obvious that there was an approximately linear relationship between temperature and pressure. This can be seen most clearly on the graph (figure 6) for the high pressure experiment. For the low pressure experiment the relationship appears to be approximately linear, but as the pressure approaches atmospheric, the relationship becomes more polynomial and the temperature appears to be more closely dependant on the absolute pressure. These observations are supported by the results pictured in the logarithmic graph (figure 7). As might be expected from Eq. 10, both of the lines have a negative gradient. It can still be seen however that, especially for the low pressure experiment, the relationship between the two variables is approximately but not exactly linear. The results from this experiment appear to show that the linear relationship is lost as the temperature increases. There are a number of factors that could start to explain this phenomenon. Firstly, experimental error needs to be taken in to account. It is important to recognise the limitations of the laboratory equipment that was used in the experiment.
In the introduction, the aims of the experiment were to firstly that there is a relationship between pressure and temperature for this particular substance, and secondly that the relationship is accurately described by the Clausius-Clapeyron Equation. Since the graphs show clear trends, in one case almost exactly linear, there is clearly some relationship between pressure and temperature. Further, that the value of hfg estimated from the results of this experiment is in close proximity to the value published in tables (which are known to follow the Clausius-Clapeyron trend)  the relationship in this experiment must also be described by the Clausius-Clapeyron equation. Conclusions * There is a definite relationship between pressure and temperature. For the low pressure experiment, this is a curved relationship which is approximately linear. For the high pressure experiment this relationship is almost exactly linear. * Results would have been affected by experimental error, including errors in the equipment itself. The most important factor appears to be the escape of the substance from the equipment during measuring * Human error would also be a factor in the results, where difficulty in making readings or parallax errors could affect their accuracy * In the derivation of the equations used in the experiment, assumptions were made which were later shown to be valid * The error in the experiment is estimated at 4.6% * Since the value of hfg estimated from the results is in close proximity to that published in tables, pressure and temperature indeed follow a trend described by the Clausius-Clapeyron equation * As such the objectives were met.
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