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Constant Volume Gas Thermometer and Pressure Coefficient

R.L.Griffith,M.R.Levi,A.Okunyan,A.Okunyan,Group 3 partners ∗

09/01/2005

Abstract

Keywords: Thermometers,Gas,Constant Volume

The temperature of a liquid was measured using a

Constant Volume Gas Thermometer. The gas that

was used was air inside a gas bulb, calibration of the

equipment was done by using the freezing point of wa-

ter at 0

o

C and the boiling point of water at 100

o

C . Acorrection had to be made to the steam point due to a

reduction of the barometric pressure at 0 degrees Cel-

sius. After the calibration was completed, regular tap

water was poured into the liquid holding vessel. Then

the temperature of the water was calculated by using

the standard equations that were derived for this ex-

periment. Two calculations were made, one was due

to the expansion of the glass in the steam calculation.

a correction was made for the pressure coefficient,

therefore equation 5 was used for this correction. and

equation 6 was used to measure the temperature of the

tap water. Experimental values agreed with theoretical

values to a very accurate degree.

Diagram

Turn screw

Gas

Liquid Container

Scale

Figure 1: Diagram of constant volume apparatus.

∗The authors would like to thank Los Angeles City College

for the use of their facilities

1 Introduction

The constant volume gas thermometer is based onthe idea that the temperature and pressure of a gasof consistent volume are directly proportional. There-fore ∆P = βP 0∆T where ∆P is the change in pres-sure, β is the pressure coefficient of the gas and ∆T

is the change in temperature. When a gas is heated

the pressure increases if it is confined to a fixed vol-ume. When a gas is cooled the pressure decreases atconstant volume. This effect is used to measure tem-perature by measuring the pressure of the gas when itis placed in thermal contact with the substance whosetemperature is being measured. If the pressure of agas in a constant volume thermometer is plotted withpressure versus temperature a linear relation is ob-served. The constant volume gas thermometer usedin this lab consisted of a large glass bulb filled with air(Hydrogen) that was connected to a tube filled withmercury and a turn screw system was used to regulatethe mercury.

1.1 Derived Equations

P 100 − P 0

100T = P T − P 0 (1)

T =(P T − P 0)100

P 100 − P 0(2)

If the pressure at T degrees is P T , then P T − P 0 alsorepresents this same change.

T = P T − P 0

β P O(3)

P T = P 0(1 + β T ) (4)

where β is the pressure coefficient.

For the calculations it will be necessary to make a cor-rection to equation 3 because when doing the steamtest we have to compensate for the expansion of theglass bulb, due to the linear expansion of glass, the

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equation that will be used is equation 5. The cor-rected value for the steam point will also be neededin the calculation.

β =P T − P 0

P 0T + β

P T

P 0(5)

T =P T − P 0

P 0β − βP T (6)

where β is the pressure coefficient and β is the linearexpansion coefficient for glass. β = 2.5× 10−5

2 Method

2.1 Equipment Used

Equipment SerialConstant Volume Gas Thermometer 51548

Steam Generator model TD-8556A n/a600 ml beaker n/aTap water n/aBarometer 179412Ice n/aMercury thermometer n/aspoon n/a

2.2 Procedure

The constant volume gas thermometer was calibratedby using ice water at 0oC and steam water at 100oC .

The ice was crushed using a electrical ice crusher, onceit was crushed it was poured into the copper jacketand filled with water. The measurements that weretaken were of the height of the mercury. Three sep-arate measurements were taken for each type of sub-stance that was placed in the copper jacket, next tapwater was poured into the copper jacket, A mercurythermometer was used to measure the temperature of the water, and three measurements were also takenfor the height of the mercury. The final trial wasfor the steam calibration. The steam generator wasfilled two-thirds of the way with tap water, and it washeated until the water was turned into steam, then a

hose was connected from the steam generator to thecopper jacket, and three measurements were taken forthe height of the mercury column. A barometer wasused to measure the atmospheric pressure at the timeof the experiment, and the temperature was also mea-sured using a mercury thermometer located next tothe barometer. For a more detailed explanation of the procedures used during this experiment please re-fer to lab:1 in the Los Angeles City College physicslab manual.

3 Results and Discussion

There are two calculations to make for this report,the first one is to calculate the pressure coefficient β

of air, and the second one is to calculate the tem-perature of the tap water using the constant volumegas thermometer, we will be using equation 5 and 6for these calculations. There are two values of P T ,P T 1 one is used when calculating for the correction of the pressure coefficient and P T 2 is used for calculatingthe temperature of the tap water. P 0 is used in bothcalculations.

P T 1 = pressure of steam put through kettle

P T 2 = pressure of tap water through kettle

P 0 = pressure of ice put through kettle

T = temperature of corrected steam point(table 2)

β = coefficient of volume expansion for glass

Item Reading

Reading of mercury thermometer 25.4(C)(A)Reading of barometer(wall) 754.8(mm)Room temperature 23.5 (C)Barometer reduced (table 1) 751.91(mm)Steam temperature (table 2) 99.7(C)

Table 2.1 Values obtained during experiment

hT (water) = −14(mm)

hT (ice) = −77.33(mm)

hT (steam) = 169.33(mm)

height of mercury column to calculate P T for steamand water temperature and P 0 for ice.

Item Calculation

P T (steam) = A + hT (steam) 1.212 (atm)P 0(ice) = A + hT (ice) .8876 (atm)P T (water) = A + hT (water) .9709 (atm)

β Eq(5) .003702 deg−1

standard value β .003663 deg−1

Experimental error ratio 1.04 %Water temp. calc. with thermometer 25.4 (C)Water temp. calc. Eq(6) 25.79 (C)Experimental error ratio 1.59 %value of 1/β (experimental) -270.12 (C)

Table 2.2 Calculated values obtained from experi-ment

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The pressure coefficient was calculated using equation5 using P T (pressure of the steam), P 0(pressure of theice), T (corrected steam temperature from table 2),and β (linear expansion coefficient for glass). The tem-perature of the tap water was calculated using equa-

tion 6 usingP T

(pressure of the water),P 0

(pressure of the ice), β (corrected value), and β (linear expansioncoefficient for glass). The following plot was createdwith the calculated data, it shows a very linear rela-tion of temperature and pressure.

Figure 2: Plot of temperature versus pressure.

4 Conclusion

The purpose of this experiment was to confirm the ac-curacy of the constant volume gas thermometer, theresults of this experiment confirmed the accuracy of the constant volume gas thermometer, error ratios for

experimental versus theoretical values were below 2percent. Some sources of error could have been ac-quired through the accuracy of the instruments, suchas the exactitude of estimating measurements. i.e themercury thermometer. some other sources of errorcould have been acquired through human errors, suchas not allowing enough time for the gas to reach equi-librium with the liquid. If the gas is not in equilibriumit will give you a wrong measurement. errors in thisexperiment were very minimal.

5 Acknowledgements

The author would like to thank everyone from group3 who helped with this experiment.

References

[1] Los Angeles City College, Lab Manual, Lab num-ber 1.

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