List of contents

INTRODUCTION………………………………………………………………………………………………………………………………….. 3

OBJECTIVES………………………………………………………………………………………………………………………………………… 3

APPARATUS…………………………………………………………………………………………………………………………………………. 3

EXPERIMENTAL PROCEDURE…………………………………………………………………………………………………………. 4

RESULTS AND DISCUSSION……………………………………………………………………………………………………………… 5

CALCULATIONS…………………………………………………………………………………………………………………………………. 6

CONCLUSION………………………………………………………………………………………………………………………………………. 9

REFERENCES………………………………………………………………………………………………………………………………………. 9

List of Figure

Figure 1  Schematic diagram of pressure and  temp. of saturated steam apparatus…………………….. 4

Figure 2  Experimental set-up of Pressure and Temp of Sat. Steam……………………………………………… 4

Figure 3  Plot absolute pressure (bar) vs. temperature(K)………………………………………………………………. 6

List of Table

Table 1  Experimental data for the pressure and temperature readings……………………………………….. 5

 

List of Symbol

 

Symbol	Description	SI Units
Texpt	Experimental Temperature value	K
Pg	Gauge pressure	kg/ms2
Pabs	Absolute pressure	kg/ms2
Patm	Atmospheric Pressure	bar
vg	Specific volume of saturated vapour	m3/ kg
hf	Specific enthalpy of saturated vapour	J / kg
vf	Specific volume of saturated liquid	m3/ kg
hfg	Latent heat of vaporisation	J / kg

 

 

 

INTRODUCTION

Saturated temperature refers to the temperature at which a specific pressure level achieves equilibrium. Saturated pressure is the pressure at which equilibrium occurs at a certain temperature. The coexistence curve is the line that separates the two phases on a pressure–temperature (P–T) diagram. The slope of the tangents of this curve is determined by the Clausius–Clapeyron relation. Following expression,

The experimental which is having boiler and other components has setup which is used to investigate the relationship between the pressure and the temperature of saturated steam. The measured value of slope of the graph (dP/dT) obtained from the experiment results can be compared to the theoretical value determined through the calculation from the steam table.

OBJECTIVES

• To obtain a relationship between the pressure and temperature of saturatedsteam, in equilibrium with water, at 5 bar gauge pressure . 
• To compare between calculated values from experiment data to the dataobtained from steam table for hfg and Vf. 
• To demonstrate the vapour pressure curve
• To Estimate the specific volume of water vapour
• Learn the use of steam table
• Learn data presentation, data interpolation

APPARATUS

A pair of cartridge electrical heater

• Bourdon gauge and an electric pressure sensor
• Platinum resistance thermometers (PRTs)
• Safety valve and
• A control/measurement box

Figure 1 Schematic diagram of pressure and  temp. of saturated steam apparatus

Figure 2 Experimental set-up of Pressure and Temp of Sat. Steam

EXPERIMENTAL PROCEDURE

1. In the apparatus, we have to fill the distilled water. After that start heating by taking the knob to extreme right.
2. As the water start heating up,before taking the readings remove the impurities like air from the boiler. From the vent valve, we can release the air.
3. Now as in the system, purely the steam is present. Start taking the readings at every interval of 0.5 bar.
4. In the controller, the knob is showing the values of the temperature in resistance(ohm) and pressure in KN/m2.
5. Take readings upto 6.5 bar gauge pressure. This is done for the heating cycle.
6. For cooling cycle, allow the boiler to reach the pressure upto 7 bar gauge pressure. After that turn off the heater by taking it to the extreme left position.
7. Take reading in the interval of every 0.5 bar gauge pressure and note it down.

RESULTS AND DISCUSSION

Table 1 Experimental data for the pressure and temperature readings

Gauge pressure	Absolute Pressure	Measured Resistance		Temperature				Saturation Temperature (From Steam table)
		Heating	Cooling	Heating		Cooling
(bar)	(bar)	(Ω)	(Ω)	(℃)	(K)	(℃)	(K)	(℃)	(K)
1.0	2.0	143.4	143.5	117.7	390.7	118.0	391.0	99.6	372.6
1.5	2.5	145.4	145.6	124.3	397.3	124.9	397.9	111.4	384.4
2.0	3.0	147.2	147.3	130.3	403.3	130.6	403.6	120.2	393.2
2.5	3.5	148.6	148.8	135.0	408.0	135.7	408.7	127.4	400.4
3.0	4.0	150.0	150.1	139.8	412.8	140.2	413.2	133.5	406.5
3.5	4.5	151.2	151.3	144.0	417.0	144.4	417.4	138.9	411.9
4.0	5.0	152.2	152.3	147.5	420.5	147.8	420.8	143.6	416.6
4.5	5.5	153.1	153.3	150.7	423.7	151.4	424.4	147.9	420.9
5.0	6.0	154.0	154.2	153.9	426.9	154.6	427.6	151.8	424.8
5.5	6.5	154.9	155	157.1	430.1	157.4	430.4	155.5	428.5
6.0	7.0	155.6	155.8	159.6	432.6	160.3	433.3	158.5	431.5
6.5	7.5	156.4	156.4	162.5	435.5	162.5	435.5	161.9	434.9

Figure 3 Plot absolute pressure (bar) vs. temperature(K)

DISCUSSION

It is critical to remove all air from the boiler before beginning the experiment. That’s because the precision of the experimental results may be influenced by the presence of air. The accurate equilibrium readings between the steam and the boiling water will not be obtained if the air is not moved. To boost the pressure, a lower water temperature will be necessary due to the partial pressure of air. Furthermore, trapped air in the boiler might cause the boiler to fail.

Ideally the heating and cooling curve should have  to be same. But here at some points we have seen that the curve is not overlapping. This is might be due to the impurities or experimental error. The apparatus temperature PT100 resistance or pressure gauge has not been calibrated properly.

CALCULATIONS

1. Find temperature in ℃

 

As the temperature readings obtained from experimental setup is in resistance.It is need to be converted into the degree celcius with the help of the below relation:-

T [℃]=0.0138Rm2−0.6926Rm−66.763

For example:- At 2 bar abs. Pressure, the value of Rm is 143.4 Ω for the heating.

T [℃]=0.0138(143.4)2−0.6926(143.4)−66.763

T [℃]= 117.7[℃]

 

1. Find absolute pressure in bar

 

P_abs = P_g + P_atm

 

Where,

 

P_abs = Absolute pressure

P_g= Gauge pressure

P_atm=  Atmospheric pressure (1 bar)

P_abs = 1 bar + 1 bar

P_abs= 2 bar

4. Find Vg_exptat 4.0 bar (absolute)

 

The specific volume of the steam at 4 bar abs. Pressure can be find out with the below relation:-

Where,

V_g,expt = Experimental value of specific volume at gaseous state.

h_fg = latent heat of vaporization

T_expt = Experimental Value of temperature for the heating or cooling.

Vf =  specific volume of saturated water

From steam table:-

h_{fg at 4 bar} = 2134 x 10³ J/kg

Hf = 605 kJ/kg

V_f = 0.37387 m3/kg

T_expt = 412.8 K

The slope of the curve  from the graph for the heating is:

Y=6E-32x^12.155

P=bT^a

 

dp/dt = baT^a-1

 

Hence, b = 6E-32 and a= 12.155

dp/dT = 6E-32 * 12.155 T^12.155-1Pa/K

= 6E-32 * 12.155 (412.8)^12.155-1

= 230404.617

vg_,expt= (2134 x 103/412.8) x (1/230404.617)+1.512

= 5169.5*4.340190804422986e-6+0.3738

= 0.3958 m3/kg

 

 

1. Linear Interpolation

 

To find the values of saturated temperature at 6.5 bar, linear interpolation need to be performed:-

 

Taking values from steam table,

y2 = Sat. Temp at 7 bar

Y1 = Sat. Temp. At 6 bar

X2 = Pressure at 7 bar

X1 = Pressure at 6 bar

Y = Sat. Temp at 6.5 bar

X = Pressure at 6.5 bar

Ts = ((165-158.8)/(7-6))(6.5-6)+158.8

Ts = 161.9  ℃

 

 

1. Percentage Error

 

%error = [(Theoretical Value – Experimental Value)/Theoretcial Value] x 100

= [(117.7 – 99.7)/117.7] x 100

= 15.29%

 

CONCLUSION

The relationship between the pressure and temperature for the saturated steam is directly proportional. The obtained PT relation for the heating is P=6E-32T^12.155 and for the cooling is P=5E-32T^12.179. As per theory, the cooling and heating curve has to be same.The error between the theoretical and experimental values is 15.29%. The cause of  error in the readings are many. Like human intervention, calibration error of measuring instrumen, room temperature and pressure, stability of material etc.

Minor errors in this lab’s data can occur in a variety of ways. The first step is to inspect and repair any leaks in the boiler. This is to guarantee that an accurate reading is taken at all times during the experiment.

REFERENCES

1. Clausius, R. (1850). “Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen” Annalen der Physik (in German).
2. Clapeyron, M. C. (1834). “Mémoire sur la puissance motrice de la chaleur”. Journal de l’École polytechnique [fr] (in French). 23: 153–190. ark:/12148/bpt6k4336791/f157.
3. Çengel, Yunus A.; Boles, Michael A. (1998) [1989]. Thermodynamics – An Engineering Approach. McGraw-Hill Series in Mechanical Engineering (3rd ed.). Boston, MA.: McGraw-Hill. ISBN 978-0-07-011927-7.
4. Iribarne, J.V.; Godson, W.L. (2013). “4. Water-Air systems § 4.8 Clausius–Clapeyron Equation”. Atmospheric Thermodynamics. Springer. pp. 60–. ISBN 978-94-010-2642-0.