Contents
Calculations & Analysis 1
Observation & Inferences 6
Sources of error 7
References 7
Calculations & Analysis
Below table gives the Temperature and Pressure reading taken while performing the laboratory tests:
T
(ᴼ C) Pabsolute
(kPa)
117.5 201.66
131.4 301.66
141.9 401.66
150.4 501.66
156.8 601.66
160.5 661.66
163.4 701.66
166.3 751.66
168.1 801.66
171.8 851.66
173.5 901.66
The graph has been plotted for the above data. This has been shown below:
The Saturation temperature has been taken from the steam tables. The Saturation Temperature and Pressure that have been taken from steam tables is shown below:
Tsat
(ᴼ C) Pabsolute
(kPa)
120.449 201.66
133.705 301.66
143.762 401.66
151.966 501.66
158.949 601.66
162.098 661.66
165.059 701.66
167.858 751.66
170.513 801.66
173.039 851.66
175.451 901.66
Based on the above table the graph is plotted between the pressure and saturation temperature.
The Value for the constants A and n are calculated Based upon the data by using the equation
Tsat = A Pnsat
This has been done manually by performing the following calculations
Tsat1 = A Pnsat1
Tsat2 = A Pnsat2
From the above two equations we get
Tsat1/ Tsat2 = (Psat1/ Psat2) n
Since all the values are available we can calculate n which comes out to be 0.161
Using this value, the value for A is calculated by putting the values in first equation,
We get A = 58
Thus the equation is Tsat = 58 P0.161sat
The percentage error in the actual steam temperature that has been obtained from laboratory experiments than that is obtained from steam table is shown below:
Tsat
(ᴼ C) T
(ᴼ C) (Tsat – T)/ Tsat
%
120.449 117.5 2.45
133.705 131.4 1.72
143.762 141.9 1.30
151.966 150.4 1.03
158.949 156.8 1.35
162.098 160.5 0.99
165.059 163.4 1.01
167.858 166.3 0.93
170.513 168.1 1.42
173.039 171.8 0.72
175.451 173.5 1.11
The saturation temperature has been calculated from the above equation. Below table shows the value of saturation temperature that has been calculated.
Tcalculated
(ᴼ C) Pabsolute
(kPa)
121.7385 201.66
136.1112 301.66
145.2929 401.66
152.1807 501.66
157.7474 601.66
160.1867 661.66
162.4465 701.66
164.5535 751.66
166.5286 801.66
168.3887 851.66
170.1475 901.66
The graph has also been plotted as shown below:
Observation & Inferences
It can be seen from the above calculation and the data that has been tabulated following observations have been made.
The graph plotted between the Pressure (kPa) on x axis and Temperature (ᴼ C) on y axis. The shape of the graph for all the graph was parabola.
The temperature as obtained from the tests is on the lower side thus the graph was lowered a bit.
The saturation temperature as obtained from the steam tables is a bit higher than the observed temperature, thus the graph was raised.
The difference in the observed value of temperature and the saturated temperature from steam table has been in the range of 1 to 3 degrees only. Thus this has not resulted in the huge variation in the graph but has just raised the graph of saturated temperature from steam table.
Also it can be seen that the calculated value of temperature from the formula has also shown deviations from temperature from steam table. In this case the difference is more than the earlier difference of steam table value and observed value. The reason for this variation is that the value of the constants n and A have been interpreted by hit and trial which accounts for a few calculation based errors due to round off and other similar issues.
The graph of the pressure with calculated value of temperature is also of the same shape. Thus this shows the values of A and n that have been calculated are not incorrect.
In the experiment however only steam temperature is calculated and not the water temperature. The assumption is that the steam has been completely converted from water that has been heated. However if the water temperature had been included it would have given more practical results. This was done in order to reduce the complexity in calculations as if the water temperature was also considered then in that case it has to be interpolated and other factors would also have to be included like saturation temperature of water and the temperature of the region between steam and water that is shown in the steam table. There is a possibility that the temperature of water and steam may be different as it has to be seen that the water has reached the critical point where it will convert to steam.
Although the water temperature has to be measured but, according to Brian Dolin, KE2 Therm Solutions, if liquid is not present in the vessel, the direct pressure-temperature relationship is no longer valid. (Dolin, 2010)
Sources of error
There are a few sources of error in this experiment. These have been listed below;
1. There might be some impurities present in the water which have resulted in the raised saturation or lowered saturation temperature. This increased or decrease saturation temperature of water due to presence of impurities cannot be discarded as there is possibility of water being contaminated by any possible item.
2. 2. There might be issue with the measuring apparatus for measuring the pressure. This is to say that the pressure gauge is faulty and may be giving incorrect values for the pressure that has been recorded.
3. There might be some issues with the gauge in the sense that there is almost constant difference between observed and steam table value of saturation temperature. Thus this can be due to some constant error coming in while performing the experiment
4. Lastly there can be some error associated with the parallax error where in the exact value of pressure as given by the apparatus is not recorded correctly. This error associated with the manual recording of data cannot be fully neglected no matter how precise value was given by the instrument. This may be due to inability of the instrument to give precise values or may be because of positioning of the measuring instrument.
References
Atkins, P. (2010). The Law of Thermodynamics. Oxford
Van Ness, H.C. (1983). Understanding Thermodynamics
Dolin, B. (2010). Basic Superheat. ‘Saturation and Subcooling’
JH14
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