Thermodynamic effects in a gas modulated Invar-based dual Fabry–Pérot cavity refractometer

Abstract

By measuring the refractivity and the temperature of a gas, its pressure can be assessed from fundamental principles. The highest performing instruments are based on Fabry-Perot cavities (FPC). Gas modulation refractometry (GAMOR)is a methodology that has the ability to reduce the influence of disturbances to such an extent that high-precision (sub-parts-per-million) assessments of pressure can be made by the use of FPCs of Invar. To allow for high accuracy assessments, it is of importance to assess the uncertainty contribution from the thermodynamic effects that are associated with the gas filling and emptying of the cavity (pV work). This paper presents a detailed scrutiny of the influence of the gas exchange process on the assessment of gas temperature on an Invar-based dual-FPC (DFPC) instrumentation. It is shown that by virtue of a combination of a number of carefully selected design entities (a small cavity volume with a bore radius of 3 mm, a spacer material with high heat capacitance, large thermal conductivity, and no regions that are connected with low thermal conductance, i.e. no heat islands, and a continuous assessment of temperature of the cavity spacer) the system is not significantly affected by pV work. Simulations show that 10 s after the filling all temperature gradients in the system are well into the sub-mK range. Experiments support that refractivity assessments initiated after 40 s are not significantly affected by the pV work. The analysis given in this work indicates that an upper limit for the influence of pV work on the Invar-based DFPC system using 100 s long gas modulation cycles is 0.5 mK/100 kPa (or 1.8ppm/100 kPa). Consequently, thermodynamic effects will not be a limiting factor when the Invar-based DFPC GAMOR system is used for assessments of pressure or as a primary pressure standard up to atmospheric pressures.

CO2 Gas Temperature Sensing near Room Temperature by a Quantum Cascade Laser in Inter Pulse Mode

“…Here, gas temperatures vary due to thermodynamic pV-work when the gas is introduced into the refractometer. Recent simulations revealed a designdependent heating of the gas by more than 50 K followed by a decay with sub-second time constants [27]. The QCLAS technique presented could be used to experimentally validate these simulations due to its excellent time resolution and non-invasive character.…”

Thermodynamic Effects in a Gas Modulated Invar-Based Dual Fabry-Pérot Cavity Refractometer Addressing 100 Kpa of Nitrogen

“…Moreover, since Invar has a three times larger volumetric heat capacity than glass (in fact, it has a more than three orders of magnitude larger volumetric heat capacity than the gas), it was concluded that the initial heating of the cavity walls will be at least two orders of magnitude smaller than that of the FLOC system. It was then also found that the increased gas temperature decays exponentially towards the cavity wall temperature with a time constant of 0.14 s and that it is within 1 mK of the temperature of the wall already after 1.5 s [7].…”

“…The gas thereafter rapidly adopts the temperature of the cavity walls. For the case with 30 kPa of N2, it was found that the decay is exponential with a time constant of 0.07 s, while, for 100 kPa, it is 0.14 s. This implies that the average temperature of the centre part of the cavity will quickly (within 1 -2 s) equalize to temperatures well within sub-mK of that of the cavity wall [7].…”

“…We have since then performed a detailed scrutiny of the influence of the gas exchange process on the assessment of gas temperature on an Invar-based dual-FPC (DFPC) instrumentation used for the gas modulation refractometry (GAMOR) methodology [7]. It was shown, by the use of simulations, that, by virtue of a combination of a number of carefully selected design entities (a small cavity volume with a bore radius of 3 mm, a spacer material with high heat capacitance, large thermal conductivity, and no regions that are connected with low thermal conductance, i.e.…”

“…It was shown, by the use of simulations, that, by virtue of a combination of a number of carefully selected design entities (a small cavity volume with a bore radius of 3 mm, a spacer material with high heat capacitance, large thermal conductivity, and no regions that are connected with low thermal conductance, i.e. no heat islands), and a continuous assessment of temperature of the cavity spacer, the assessment of pressure is not significantly affected by pV-work when pressures up to 100 kPa are addressed by the use of gas modulation cycles of 100 or 200 s [7].…”