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Physics
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1026

SATURATION PRESSURE MEASUREMENT

Background Theory

The temperature at which a liquid changes from a liquid phase to a vapor phase usually varies with temperature. The relationship between saturated water temperature and its temperature is of great importance, especially when establishing the thermodynamic properties of a steam. The point of saturation of water is the point where phase change occurs – either from liquid to vapor or vapor to liquid. These conditions of water pressure and temperature at which phase change occurs can be plotted on a graph to obtain a saturation line. When a graph of absolute pressure (P abs) against absolute temperature (T abs), a smooth curve is produced. Over a limited range of liquid pressure, a good fit of the curve can be obtained using the equation shown below, which describes the behavior of liquid properties. …………………………… (i)

For a given range of pressures, there are specific values of coefficients and which minimize the differences between the curve equation and the measured points from the experiment. These differences may arise due to experimental errors and sometimes, the real liquid behavior may not perfectly match the equation. If the curve is linearized, one can obtain the best-fit values of these two coefficients. This is usually done by taking the logarithms of equation (i). …………………… (ii)

The values and are the gradient and intercept of the graph of P abs versus (1/T) respectively. To determine the relationship that exists between the saturation temperature of water and the pressure of the steam, several corresponding values of temperature and pressure need to be measured and plotted on a graph.

Objective

This lab experiment was performed with the following objectives:

• To gain an understanding of the principles of saturation pressure measurement.

• To investigate the relationship that exists between the pressure and temperature of vaporization of water.

• To establish the accuracy of the saturation data obtained using basic equipment.

Experimental
Method

A pressurized vessel was filled with water and heated to the boiling point. The thermometer output and pressure sensor were read and recorded at intervals of 2 minutes, and the values of the thermometer output converted into temperature using the tables provided. The procedure was repeated during the cooling process to obtain graphs of absolute temperature against time during heating and cooling.

The pressurized vessel was filled with water and heated to the boiling point. The pressure reading and temperature resistance readings were taken from the pressure sensor and the platinum temperature sensor respectively and recorded in a table. The values of temperature resistance were converted into temperature and the graph of abs versus (1/T) plotted. On the same graph, calculated values of abs using equation (ii) verses (1/T) were plotted for comparison.

Results and Calculations

PART B: Principles of saturation pressure measurement

Table 3: Barometric pressure (kN/m2) during heating

 Elapsed time Measured output Corrected output Absolute temperature Pressure Absolute Pressure Actual temperature 0

Using the resistance bridge correction chart to obtain the corrected output;

Rm1 = 139.9 and interpolating between 139 and 140 Ω;

RC1 = 138.71 RC1= 139.241Ω

Using the PT100 platinum resistance Thermometer reference chart the values of absolute temperature are;

RC1 = 139.241Ω, interpolating between 138.50Ω and 139.26 Ω

Tabs= = 375.124 K

Absolute pressure Pabs= Pressure P1 + Atmospheric pressure Patm

Patm = 102.5 kPa = 102.5 kN/M2

Pabs= 28+102.5= 130.5kN/M2

Taking the assumption that the measured steam temperature is equivalent to vapor point, the actual steam temperature is obtained from the graph of vapor point of water. Below is a graph of absolute temperature (Tabs) and actual absolute temperature(Tact) against time plotted on the same axes for the values in table 3 above. Figure 2: Graph of indicated absolute temperature (Tabs) and actual absolute temperature(Tact) against time (mins) during heating

Table 4: Barometric pressure during cooling

 Elapsed time Measured output Corrected output Absolute temperature Pressure Absolute Pressure Actual temperature 0

Figure 3 below shows the graph of absolute temperature (Tabs) and actual absolute temperature(Tact) against time plotted on the same axes for the values in table 4 above Figure 3: Graph of indicated absolute temperature (Tabs) and actual absolute temperature(Tact) against time (mins) during cooling.

Conclusion

In figure 2 during heating, the indicated temperature line is below the actual temperature line, indicating small differences between the indicated output temperature of the platinum resistance thermometer and the actual temperature at any given time. From the graph in figure 2, the thermal lag is approximately 1.5 minutes. In figure 3 during cooling, the actual temperature is below the indicated temperature. This difference is what is referred to as the thermal lag.

Knowing the thermal lag is significant in the sense that we can now estimate the correct saturation pressure of the fluid. Thermal lag can be reduced by reducing the thermal mass or thermal capacity of the temperature sensor, and also using materials with high heat conductivity (McGee, 1988).

PART C: Concept of a saturation line

Table 1: Measuredvalues of resistance and pressure

 Measured output Corrected output Pressure Absolute temperature Absolute Pressure Pabs (kN/M2) Using the resistance bridge correction chart to obtain the corrected output;

Rm1 = 149.1, interpolating between 149Ω and 150Ω

RC1= 151.17 + ( RC1 = 151.303 Ω

Using the PT100 platinum resistance Thermometer reference chart the values of absolute temperature are;

RC1 = 151.303Ω, interpolating between 150.57Ω and 151.33 Ω

Tabs= = 407.079 K

Therefore T-1= 0.00246  Below is a graph of measured and calculated verses plotted from the values in table 1 and 2 respectively. Figure 1: Graph of measured (table 1) and calculated (table 2) In P abs versus 1/T

From the graph:

a = -4617.8

Po (Y intercept) = 17.177

Using the equation ln Pabs = ln Po + a with a = -4617.8, Po = 17.177 to calculate the values of ln Pabs and plotting in the same axes of figure 1 above;

Table 2: Calculated values of In P abs

 Calculated values of Conclusion

Both graphs in figure 1 show very small differences in their trends, suggesting that the describing equation (ii) has high accuracy compared with the measured values.

References

McGee, T. D., 1988. Principles and Methods of Temperature Measurement. London: John Wiley & Sons.