Mercet Boiler 2

1.0 Objectives: The main idea was to study the relationship between pressure & temperature, for saturated steam in equilibrium with water.

2.0 Theory: Marcet boiler: It is about an instrument for measuring the vapor pressure of water. A small spherical boiler is fitted with a thermometer and a long mercury manometer. You half-fill it with water, and then heat it. The thermometer and manometer give a sequence of pressures and the matching boiling-point temperatures. The instrument is limited by the height of the manometer. If it's 2½ feet high, you can measure up to twice atmospheric pressure. If it's five feet high, you can go to three atmospheres, and so on. See fig.1

From the experimental data, taken in the lab, the P-T diagram can be drawn. Furthermore, we can use it to investigate the ClausiuClaperon relation, which states that: (dT/dP) sat. = (T * vfg) / hfg , such that; a) dT/dP: is the slope of the P-T curve, for saturated steam in equilibrium with water. b) T: is the absolute temperature (K). c) vfg = vf - vg. d) hfg = hf - hg. e) vf : is the specific volume for saturated liquid, (m3/kg). f) vg : is the specific volume for saturated vapor, (m3/kg). g) hf : is the specific enthalpy for saturated liquid, (kJ/kg). h) hg : is the specific volume for saturated vapor, (kJ/kg).

3.0 Calculations & Results: Readings were taken as the pressure was increasing, from 0 to 5-bar, and decreasing, from 5 to almost 0, but it did not reach 0. The following table was used to draw the required graphs. Gauge pressure (bar).

Absolute pressure (bar).

0 1 2 3 4 5

0.933 1.933 2.933 3.933 4.933 5.933

Steam temp. Inc. Dec. press. press. Temp. Temp. 0 0 C C 95 --109 110 121 126 133 137 142 145 149 150

Table 1: Barometric pressure.

Mean temperature oC.

95 109.5 123.5 135 143.5 149.5

Mean Temp. VS Absolute pressure

Mean Temp. C

160 150 4.933

140

3.933

130 2.933

120 110 100 90

5.933

1.933 0.933

0.933

1.933

2.933

3.933

4.933

5.933

Absolute pressure (bar)

Calculating the slope from the graph, at three different points, gives: At (2.5, 114.97) & (1.5, 103.94): dT/dP = 11.03. At (3.5, 126.00) & (4.5, 137.03): dT/dP = 11.03. At (5.5, 148.05) & (4.5, 137.03): dT/dP = 110.3. Calculating the slope from the table, at three different points, gives: At (0.933, 95) & (1.933, 109.5): At (1.933, 109.5) & (2.933, 123.5): At (2.933, 123.5) & (3.933, 135):

dT/dP = 14.5. dT/dP = 14.0. dT/dP = 11.5.

The difference in the results may be due to the fact that the curve represents the best fit for the readings, and not all the points are on the curve.

4.0

Discussion & Conclusion:

In this experiment, we learned the relationship between temperature and pressure for saturated steam in equilibrium with water; and was directly proportional.