Properties of Water

And The First Law of Thermodynamics

In Closed and Open Systems

2

1.Pre-lab

1. The purpose of the U-trap is to prevent condensate escaping from the graduated cylinder as

steam. We want to measure the steam condensed during the timed test.

2. Qout is the fugitive heat energy lost from the boiler during each ten-minute test period. Rate

Qout is the average rate at which fugitive heat leaves the boiler.

3.

,

1 2

( )

( )

( ) ( )

( )

( ) ( )

out open in g f

cvcv

f in out g

out in g f

f in out f g

Q Q m h u

dEQ W m h h

dt

m u Q Q m h

Q Q m h u

m h Q Q m h h

Steady state =>

( )

( ( ))

out in f g

out in g f

Q Q m h h

Q Q h u pv

3

2. Introduction:

The main objective of this lab is to explore the properties of the water and the first law

of thermodynamics in both closed and open systems. The first part is to measure the T-p

saturation curve of water with and without air trapped in a boiler. Second I have to determine

the heat lost from the boilers wall to surrounding air, as a function of boiler temperature,

while the boiler is operating at steady state closed system. Finding the same loss but now

operating at steady state open system using the mass of condensate which leaves the control

volume. Finally to verify the first law comparing the fugitive losses when the system is closed

and when it is open.

3. Theory:

There are two fundamental things underlying this experiment: first law of

thermodynamics and T-p diagrams in particular the saturation curves for water.

∆KE+ ∆PE+ ∆U= Q- W (1)

∆KE, ∆PE, W are equal to zero for that specific experiment. So fugitive losses for

closed system will depend only on the electrical power put into the system multiplied by the

heater’s ON time:

Qout,closed = Qin = ErmsIrms∆t (2)

Erms is the value of heater’s voltage in [V]

Irms is the value of heater’s current in [A]

∆t is the time when the heater is ON in [s]

The average rate at which heat leaves the system during the ten minute test period is

given by the equation:

Average Rate Qout,system=Qout,closed/600 (3)

Where Qout,close is the same from equation (2)

Similarly based on the first law of thermodynamics the heat lost from the boiler to the

surroundings for the open system is. Also I am assuming that the boiler is a control volume.

Qout,open = Qin - ∆m(hg - uf ) = ErmsIrms∆t -∆m(hg - uf ) (4)

Where Qin is calculated the same way as in equation (2), and the extra term accounts

for the energy lost by means of mass transfer across the open system. ∆m is the total mass of

the condensate which leaves the control volume, hg is the specific enthalpy of the saturated

water vapor, and uf is the specific internal energy of the saturated liquid water. The average

rate at which heat leaves the system is:

Average Rate Qout,system = Qout,system/600 (5)

4

The saturated p-T curves will be used to compare the actual tabulated data with the

numbers collected in the experiment.

4. Procedure:

Closed system:

First we used both heaters to heat the boiler to temperature of 110oC. Then we had to

keep the temperature as close to constant by turning on and off one of the heaters. Keeping

the temperature constant at 100oC (±0.4) for ten minutes (the cumulative heater ON time).

When the heater was on we recorded the heater voltage, current, the gage pressure in the

voltage. When the ten minutes were up we recorded the total ON time of the heater. Finally

release the air trapped in the boiler by opening the stop valve and the throttling calorimeter

valve, until all air is purged.

We repeated this procedure one more time for 110oC and for 115

oC.

Open system:

We used our last try to perform the open system measurements. We placed a graduated

cylinder under the end of the condensate so that a U-trap is formed. Then we opened the

cooling water valve. Keeping the temperature constant as it was in the last part (115oC) using

one of the heaters. During this process the throttling calorimeter valve was open. Keeping the

temperature constant, and when the heater is on we recorded heater’s voltage, current and also

the boiler pressure. Then we measured the amount of condensate collected in the graduated

cylinder during the ten-minute period. In the end we recorded again the total time when the

heater was on.

5. Data and Analysis:

1. The data collected during the lab for different pressures at different temperatures is shown

in table 1. Note that the pressure was converted from gage to absolute and also from psi to

kPa. The reason for the second conversion is that the temperature obtained was in Celsius.

Table 2 consist with the tabulated values from the book (table A-2). In graph one there are 4

series of data. The data collected during my lab separated for closed system with air and

closed system without air, and all other data collected during the other labs again separated

for closed system with air and closed system without air.

2. The values for fugitive heat lost from the boiler to the surroundings during each ten minute

test period can be found in table 1. The average rate of heat lost is in the same table. They

were calculated using equations (2) and (3) respectively.

3. In order to calculate the fugitive heat lost from the boiler to the surroundings during each

ten minute test for the open system I used equations (4) and (5). The values can be found in

table 3.

To find hg and uf I used table A-3 from the book, where I knew the temperature. For part of

the calculations I needed to interpolate between the rows. The formulas I used and

calculations I made are attached in the Appendix.

5

4. Graph 2 in the Appendix shows a plot of the average rate of heat transfer to the

surroundings as a function of the boiler temperature. Different symbols were used to

distinguish between the results from my group, the results from all other groups, and also

when the system is closed or open.

6. Questions:

1. For the closed system, the p-T graph is shown in graph 1. Experimental results are really

close to the accepted values from the saturation table. The data collected follows the pattern

of the curve described by the accepted values. The error is really small: around 3%. The only

values which do not match the accepted ones are when the boiler has air inside.

2. The experimental results obtained tell us that is always important to allow 3-5% uncertainty

when using values from tables for real life applications.

3. The air trapped in the boiler prevented us to take good approximations in first place. The

reason for that is that when we have non-condensable gases such as air trapped inside of a

heat transfer device, such as boiler, that air prevents heat transfer to occur. And as our data

shows only the pressure is increasing while the temperature is staying constant. Therefore I

can conclude thatt it is really important to remove all non-condensable gases such as air from

the boiler in this case, or in general from all other heat transfer devices if one wants to make

use of values for pressure and other properties that come from tables( e.g. table A-3 from the

book).

4. As shown in graph 2, the obtained values for fugitive heat transfer from the system to the

surroundings fluctuated as temperature increases. Overall they seem to be slightly increasing

with temperature.

5. In general graph 2 shows that the results for the closed system are increasing with

temperature. The results for the open system, however, seems to be everywhere but within the

same range of the system. If we ignore uf equation (5) will become:

Qout,open = Qin - ∆m(hg) (6)

The results from this equation are in the last two columns in table 3. If we plotted this values

it will be clear that it still follow a pattern but now are vertically displaced much lower than

the results for the closed system.

7. Discussion:

The behavior of absolute pressure as a function of temperature is plotted on graph 1 in

the appendix. In the very left of the graph there are different pressure values align vertically

and are significantly off the values given from the saturation table. This discrepancy is due to

6

the fact that this values were collected when there was air into the boiler. This effect is very

important and tells us to always get rid of the air into such systems if we want to use steam

charts such as the one in the book. All other values were very close to the accepted ones. The

average error is around 3% which tells me that we performed the experiment really well.

Graph 2 is a plot of average rate of fugitive heat from the system to the surroundings as a

function of temperatures analyzed in the lab. The graph shows agreement between the values

obtained from the closed system and the open system, in accordance to the first law. Overall

the data shows that they follow a similar patter, and between 130oC and 150

oC they almost

match. If we take out the internal energy from equation (4) it will not be so close as I

discussed already in question 5. This shows that the first law is valid for both open and closed

systems. For closed system the heat transfer to the surrounding is given by the electric power

coming in to the systems through the heaters. For the open system steam is allowed to escape

the system and carry some energy with it. As a result approximately the same amount of heat

flows out of the system at specific temperature.

8. Conclusion:

In this lab, thermodynamics properties of water and applications of first law of

thermodynamics were explored. The experiment consists of measuring voltage, currant

pressure and heater’s time ON at different temperatures for two kind of systems – closed and

open. Through theoretically derived equations the collected data was used to calculate heat

transfer between the systems and the surrounding. Two different kind of plots were analyzed

– absolute pressure as a function of temperature and rate of heat transfer as a function of

temperature. As discussed in the discussion section the results found were very close to what

It was expected in general. Some of the obtained values were a lot different but there is

always a possibility of human error in such experiment. In general the lab can be considered

successful.

7

Appendix

Formulas needed for table 1:

Pabs = Pgage+Patm

Patm psi 14.696

Conv. Fact 1psi to kPa 6.8948

Qout,closed= Erms*Irms*∆t = V*I*∆t

rate Qout,closed =Qout,closed/600

Table 1:

T

[°C]

V

[Volt]

I

[A]

P

[psi]

Pabs

[psi]

Pabs

[kPa] Δt [s]

Δm

[g]

Qout,closed

[KW]

Ave rate

Qout,closed

[kw/s]

Group

1

Closed system with

air 110 208.10 10.3 20.0 34.7 239.2 187.1 --- 401.1 0.67

Closed system

without air 110 207.90 10.3 7.4 22.1 152.3 208.9 --- 447.4 0.75

Closed system

without air 115 208.90 10.3 11.4 26.1 179.9 202.9 --- 436.5 0.73

Open system without

air 115 208.60 10.3 11.2 25.9 178.5 --- 421.0

Group

2

Closed system with

air 110 208.10 10.3 20.0 34.7 239.2 187.1 --- 401.1 0.67

Closed system

without air 110 208.70 10.3 7.8 22.5 155.1 164.5 --- 353.6 0.59

Closed system

without air 120 206.90 10.2 15.2 29.9 206.1 210.9 --- 445.1 0.74

Open system without

air 120 207.00 10.2 15.0 29.7 204.7 --- 423.0

Group

3

Closed system with

air 110 209.30 10.3 19.0 33.7 232.3 184.7 --- 398.1 0.66

Closed system

without air 110 210.30 10.4 8.0 22.7 156.5 200.5 --- 438.4 0.73

Closed system

without air 125 209.20 10.3 21.0 35.7 246.1 214.2 --- 461.6 0.77

Open system without

air 125 209.20 10.4 20.8 35.5 244.7 --- 422.0

Group

4

Closed system with

air 110 210.10 10.4 13.0 27.7 191.0 228.0 --- 498.2 0.83

Closed system

without air 110 210.00 10.3 7.6 22.3 153.7 185.2 --- 400.5 0.67

Closed system

without air 130 209.10 10.3 26.0 40.7 280.6 224.4 --- 483.4 0.81

Open system without

air 130 208.90 10.3 25.2 39.9 275.1 --- 392.0

8

Group

5

Closed system with

air 110 206.70 10.3 13.0 27.7 191.0 260.8 --- 555.2 0.93

Closed system

without air 110 208.50 10.3 7.3 22.0 151.7 203.4 --- 436.8 0.73

Closed system

without air 135 208.80 10.3 32.0 46.7 322.0 224.6 --- 482.9 0.80

Open system without

air 135 209.00 10.3 32.0 46.7 322.0 --- 355.0

Group

6

Closed system with

air 110 206.70 10.3 13.0 27.7 191.0 260.8 --- 555.2 0.93

Closed system

without air 110 209.30 10.3 7.1 21.8 150.3 192.4 --- 414.8 0.69

Closed system

without air 140 209.10 10.3 39.4 54.1 373.0 268.4 --- 578.0 0.96

Open system without

air 140 209.50 10.3 39.0 53.7 370.2 --- 379.0

Group

7

Closed system with

air 110 210.30 10.4 9.2 23.9 164.8 212.1 --- 463.8 0.77

Closed system

without air 110 209.10 10.3 7.5 22.2 153.0 145.2 --- 312.8 0.52

Closed system

without air 142 211.30 10.4 44.9 59.6 410.9 215.3 --- 473.1 0.79

Open system without

air 142 209.10 10.3 41.0 55.7 384.0 --- 395.0

Group

8

Closed system with

air 110 209.30 10.3 13.4 28.1 193.7 155.7 --- 335.6 0.56

Closed system

without air 110 208.30 10.3 7.4 22.1 152.3 174.8 --- 375.1 0.63

Closed system

without air 144 208.00 10.2 46.9 61.6 424.7 260.3 --- 552.3 0.92

Open system without

air 144 209.30 10.3 45.0 59.7 411.6 --- 364.5

Group

9

Closed system with

air 110 209.30 10.3 13.4 28.1 193.7 155.7 --- 335.6 0.56

Closed system

without air 110 207.90 10.3 7.2 21.9 151.0 162.6 --- 348.1 0.58

Closed system

without air 146 209.20 10.3 49.2 63.9 440.5 245.5 --- 528.9 0.88

Open system without

air 146 209.10 10.3 48.5 63.2 435.7 --- 385.0

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Table 2:

Data from

saturation table

A-2

T [oC] P [kPa]

110 143.3

120 198.5

130 270.1

140 361.3

150 475.8

10

Graph 1:

100

150

200

250

300

350

400

450

500

100 110 120 130 140 150 160

Ab

solu

te P

ress

ure

[kP

a]

Temperature [oC]

Boiler pressure vs Boiler temperature Closed system test

Saturation table

Group 1 with air

Group 1 without air

All Groups with air

All Groups without air

11

Table 3:

This table is only for open system. The formulas used are written in the theory part.

Calculating hg and uf from saturation table A-2

* for some of the temperatures I will need to interpolate, so I will use this

formula:

a d

b unknown

c e

T [oC]

hg

[kJ/kg] uf [kJ/kg]

∆m

[kg]

∆t

[s]

V

[Volt] I [A]

Qin

[kW]

Qout,open

[kW]

Ave

rate

Qout,open

[kW/s]

Qout,open

without

uf [kW]

Ave rate

Qout,open

without uf

[kW/s]

115 2698.9 482.32 0.421 600 208.60 10.3 1289.1 355.97 0.593 152.91 0.255

120 2706.3 503.5 0.423 600 207.00 10.2 1266.8 335.06 0.558 122.08 0.203

125 2713.4 524.76 0.422 600 209.20 10.4 1305.4 381.80 0.636 160.35 0.267

130 2720.5 546.02 0.392 600 208.90 10.3 1291.0 438.61 0.731 224.57 0.374

135 2727.2 567.38 0.355 600 209.00 10.3 1291.6 524.88 0.875 323.46 0.539

140 2733.9 588.74 0.379 600 209.50 10.3 1294.7 481.69 0.803 258.56 0.431

142 2736.4 597.33 0.395 600 209.10 10.3 1292.2 447.31 0.746 211.36 0.352

144 2738.9 605.92 0.364 600 209.30 10.3 1293.5 516.00 0.860 295.14 0.492

146 2741.4 614.51 0.385 600 209.10 10.3 1292.2 473.39 0.789 236.80 0.395

e d unkown dunknown

c a b a

12

Graph 2:

0.45

0.55

0.65

0.75

0.85

0.95

100 110 120 130 140 150

rate

Qo

ut,

clo

sed

[kW

/s]

Temperature [oC]

Average Rate Qout vs Temperature for both Closed and Open System

Group 1 rate Qout,closed

Group 1 rate Qout,open

All Groups rate Qout,open

All Groups rate Qout,closed

13