When using helium vapor bulbs under 30K, what is the formula to convert from PSI or Torr to degrees Kelvin?
3 Comments
Dr. Randall F. Barron
August 1, 2008
There are 3 very good computer programs for calculating the pressure-temperature relationship for helium:
o ALL PROPS. Center for Applied Thermodynamic Studies
College of Engineering
University of Idaho
Moscow, ID 83843
o NIST-12. Office of Standard Reference Data
National Institute of Standards & Technology
Gaithersburg, MD 20899
o HEPACK. Cryodata, Inc.
P.O. Box 173
Louisville, CO 80027
e-mail:jpersichetti@htess.com
Phone: (303) 472-2530
The critical temperature of He-4 is 5.2 K and the critical pressure is
227 kPa (33.0 psi), so there is no “vapor pressure” for He-4 for temperatures above 5.2 K. Above this temperature, the thermometer acts as a constant-volume gas thermometer, not as a vapor-pressure thermometer.
The He-4 vapor pressure equation is given in:
B.W. Mangum and G.T. Furukawa, “Guidelines for Realizing the International Temperature Scale of 1990 (ITS-90),” NIST Technical Note 1265, Aug. 1990,
pg. 92.
The constants Ao, A1, …, A9, B, and C are given in the above-mentioned reference, Table 3, pg. 93.
For the thermometer operating in the constant-volume gas thermometer mode, the temperature-pressure relationship is given by eqn. (6.21), pg.
322 of:
R.F. Barron, CRYOGENIC SYSTEMS, Oxford University Press, New York, (1985).
p(Ts/ps)[1 + B(Ts)ps]/[1 + B(T)p]
T = ———————————
Vo Ts p 1 + B(Ts)ps
1 + —– [1 – — ———– ]
V To ps 1 + B(To)p
Ts = temperature at the calibration point
ps = corresponding pressure at the calibration point
B(Ts) = second virial coefficient for He-4 at Ts
B(T) = second virial coefficient for He-4 at T
To = dead-volume temperature (usually ambient temp.)
B(To) = second virial coefficient for He-4 at To
Vo = dead volume
V = sensing element volume
p = gauge pressure indication
The second virial coefficient for He-4 is (see eqn. 6.26 of Cryogenic
Systems, pg. 323)
You can find the complete information in Modern Gas-Based Temperature and Pressure Measurements, Franco Pavese and Gianfranco Molinar, Instituto de Metrologia IMGC, Turin, Italy, Plenum Press, New York and London 1992, Appendix A, page 447. This book also contains a lot of other useful information concerning the He bulb.
Are you using the saturated vapor pressure of liquid helium as your temperature indicator? If so, the temperature-pressure relationship is in any standard cryogenics physics text, say Barron, “Cryogenic Systems” or Van Sciver, “Helium Cryogenics.” Van Sciver has a table of vapor pressure vs. temperature in the appendix. If you are using a constant-volume bulb above the critical point, Barron has a good discussion in Chapter 6. His first edition has a chart of corrections above the critical point. The correction to the ideal gas law is quite small down to 20 or 30 Kelvin, and readily calculable below that.
3 Comments
Dr. Randall F. Barron
August 1, 2008There are 3 very good computer programs for calculating the pressure-temperature relationship for helium:
o ALL PROPS. Center for Applied Thermodynamic Studies
College of Engineering
University of Idaho
Moscow, ID 83843
o NIST-12. Office of Standard Reference Data
National Institute of Standards & Technology
Gaithersburg, MD 20899
o HEPACK. Cryodata, Inc.
P.O. Box 173
Louisville, CO 80027
e-mail: jpersichetti@htess.com
Phone: (303) 472-2530
The critical temperature of He-4 is 5.2 K and the critical pressure is
227 kPa (33.0 psi), so there is no “vapor pressure” for He-4 for temperatures above 5.2 K. Above this temperature, the thermometer acts as a constant-volume gas thermometer, not as a vapor-pressure thermometer.
The He-4 vapor pressure equation is given in:
B.W. Mangum and G.T. Furukawa, “Guidelines for Realizing the International Temperature Scale of 1990 (ITS-90),” NIST Technical Note 1265, Aug. 1990,
pg. 92.
T{K} = Ao + A1 [(ln p{Pa} – B)/C] + A2 [ln p{Pa} – B)/C]^2 + . . . +
A9 [ln p{Pa} – B)/C]^9
The constants Ao, A1, …, A9, B, and C are given in the above-mentioned reference, Table 3, pg. 93.
For the thermometer operating in the constant-volume gas thermometer mode, the temperature-pressure relationship is given by eqn. (6.21), pg.
322 of:
R.F. Barron, CRYOGENIC SYSTEMS, Oxford University Press, New York, (1985).
p(Ts/ps)[1 + B(Ts)ps]/[1 + B(T)p]
T = ———————————
Vo Ts p 1 + B(Ts)ps
1 + —– [1 – — ———– ]
V To ps 1 + B(To)p
Ts = temperature at the calibration point
ps = corresponding pressure at the calibration point
B(Ts) = second virial coefficient for He-4 at Ts
B(T) = second virial coefficient for He-4 at T
To = dead-volume temperature (usually ambient temp.)
B(To) = second virial coefficient for He-4 at To
Vo = dead volume
V = sensing element volume
p = gauge pressure indication
The second virial coefficient for He-4 is (see eqn. 6.26 of Cryogenic
Systems, pg. 323)
B(T) = 0.0072929 T^-5/4 (1 – C1 T^-1/2 – C2/T + C3 T^-3/2)
C1 = 3.04135
C2 = 14.14250
C3 = 17.35052
Units for B(T) are (1/kPa) and T is in kelvins.
Vladislav Benda
August 1, 2008You can find the complete information in Modern Gas-Based Temperature and Pressure Measurements, Franco Pavese and Gianfranco Molinar, Instituto de Metrologia IMGC, Turin, Italy, Plenum Press, New York and London 1992, Appendix A, page 447. This book also contains a lot of other useful information concerning the He bulb.
Dr. Peter Mason
August 1, 2008Are you using the saturated vapor pressure of liquid helium as your temperature indicator? If so, the temperature-pressure relationship is in any standard cryogenics physics text, say Barron, “Cryogenic Systems” or Van Sciver, “Helium Cryogenics.” Van Sciver has a table of vapor pressure vs. temperature in the appendix. If you are using a constant-volume bulb above the critical point, Barron has a good discussion in Chapter 6. His first edition has a chart of corrections above the critical point. The correction to the ideal gas law is quite small down to 20 or 30 Kelvin, and readily calculable below that.