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Investigation of High-Stability Temperature Control in Primary Gas Thermometry

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Abstract

We presented a relationship between the temperature control and measurement stability limit and the temperature resolution, particularly for using rhodium-iron resistance thermometers and AC resistance bridges. Based on this, temperature control was investigated and demonstrated in primary gas thermometry under various working conditions. With optimized parameters, micro-Kelvin level temperature control stability was realized in the temperature region from 5 K to 24.5 K. The temperature control stabilities are better than 8 µK over 180 h with an integration time of 33.6 s in the concerned temperature range, closing to the limit that the sensors and the instruments can control and measure. These stabilities were significantly improved about (44 ± 8)% at 24.5 K and (70 ± 7)% at 5 K comparing with our previous work (Chen et al., Cryogenics, 2019, 97: 1–6).

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Abbreviations

AC:

Alternating current

GM-PTC:

GM type pulse tube cooler

ITS-90:

International Temperature Scale of 1990

NPL:

National Physical Laboratory

PID:

Proportion-Integration-Differentiation

RTRT:

Rhodium-iron resistance thermometer

SI:

International System of Units

SPRIGT:

Single-pressure refractive-index gas thermometry

c :

Voltage noise coefficient/nVHz−1/2·Ω−1

I :

Excitation current/mA

I c :

Excitation current of the controlled NPL2 sensor/mA

I m :

Excitation current of the measuring NPL1 sensor/mA

N :

Total measured data point number

n :

Transformer ratio, i.e. Rt/Rs, or measuring index

p :

4He gas pressure in the resonator/kPa

R 1 :

Potential lead resistance of standard resistor/Ω

R 2 :

Potential lead resistance of temperature sensor/Ω

R 2 :

Goodness of Fit

R e :

Extra resistance/Ω

R cl :

Total current lead resistance/Ω

R out :

Bridge output impedance/Ω

R pl :

Total potential lead resistance/Ω

R s :

Resistance of standard resistor/Ω

R t :

Resistance of temperature sensor/Ω

S :

Sensitivity/Ω·K−1

t :

Measuring time/h

T :

T90 Temperature/K

T − :

Temperature/K, smaller than the average one (T>Tavg)

T + :

Temperature/K, larger than the average one (T>Tavg)

T avg :

Average temperature/K

T set point :

Temperature of the set point/K

ΔT :

Temperature difference/K

u(σ T) :

Standard uncertainty of the measured temperature stability/µK

u(σ T,L) :

Standard uncertainty of the temperature stability limit/µK

V A :

Analogue output voltage of the F18 bridge/V

x :

The x-th measured data point

α :

Temperature coefficient of the thermometer/K−1

β :

Ratio of the second derivative to the first derivative of resistance with respect to temperature/K−1

δ R :

Resistance resolution/µΩ

δ T :

Resolution of the temperature sensor/µK

δ v :

Specific voltage resolution of the AC

δ v :

bridges/nV·Ω−1

δ V :

Voltage resolution of the AC bridges/nV

σ T :

Measured temperature stability/µK

σ T,L :

Temperature stability limit/µK

σ R,T,L :

Relative temperature stability limit

τ :

Integration time/s

τ g :

Generated integration time/s

A:

Analogue output

avg:

Average value

c:

Controlled

L:

Limit value

m:

Measuring

R:

Relative values or resistance

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Acknowledgment

This work was supported by the National Key Research and Development Program of China (Grant No. 2016YFE0204200), the National Natural Science Foundation of China (Grant No. 51627809 and 52006231), the International Partnership Program of the Chinese Academy of Sciences (Grant No. 1A1111KYSB20160017), the Scientific Instrument Developing Project of the Chinese Academy of Sciences (Grant No. ZDKYYQ20210001), the European Metrology Research Program (EMRP) Joint Research Project 18SIB02 “Real K”, the CAS Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry (Grant No. CRYOQN202110). This work was also supported by the project “15SIB02 InK 2” which has received funding from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme. Changzhao Pan is grateful for the funding provided by a Horizon 2020 Marie Skłodowska Curie Individual Fellowship 2018 (No. 834024).

The authors are deeply grateful to our colleague Ying Ma for expert technical assistance. We gratefully acknowledge Richard Rusby from NPL for calibrating three rhodium-iron resistance thermometers, sharing his long experience and giving constant advice on temperature measurements.

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Author notes

  1. These authors contributed equally to the work and should be regarded as co-first authors.

Authors and Affiliations

  1. TIPC-LNE Joint Laboratory on Cryogenic Metrology Science and Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, 100190, China

    Jiangfeng Hu, Haiyang Zhang, Yaonan Song, Changzhao Pan, Bo Gao, Wenjing Liu, Dongxu Han, Zhen Zhang, Ercang Luo & Laurent Pitre

  2. Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing, 100190, China

    Jiangfeng Hu, Haiyang Zhang, Yaonan Song, Bo Gao, Wenjing Liu, Zhen Zhang & Ercang Luo

  3. University of Chinese Academy of Sciences, Beijing, 100490, China

    Jiangfeng Hu, Yaonan Song, Wenjing Liu & Ercang Luo

  4. Laboratoire national de métrologie et d’essais-Conservatoire national des arts et métiers, F93210, La Plaine-Saint Denis, Paris, France

    Changzhao Pan & Laurent Pitre

  5. School of Mechanical Engineering, Beijing Institute of Petrochemical Technology, Beijing, 102617, China

    Dongxu Han

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  1. Jiangfeng Hu
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Corresponding authors

Correspondence to Haiyang Zhang or Bo Gao.

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Hu, J., Zhang, H., Song, Y. et al. Investigation of High-Stability Temperature Control in Primary Gas Thermometry. J. Therm. Sci. 31, 765–776 (2022). https://doi.org/10.1007/s11630-022-1533-9

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  • DOI: https://doi.org/10.1007/s11630-022-1533-9

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