Instrumentation & Measurement Magazine 23-3 - 12

pascal can also be expressed as Pa = N/m2 = J /m3, where N is
the symbol for the SI unit of force, the newton, and J is the symbol for the unit of energy, the joule.
Through four centuries, pressure has been measured
with mercury manometers which, by the 21st century, have
achieved a high degree of perfection [5]. Simply put, if one
end of a U-tube that contains mercury is evacuated, the pressure p on the other end is proportional to the height difference
Δh between the evacuated tube and the pressurized tube. To
first order,
	

p = ρ Hg gΔh.	(4)

The density of mercury ρHg (about 13 600 kg/m3) must be
accurately known as a function of temperature, and the local gravitational acceleration g (about 9.8 m/s2) must also be
accurately known. The pressure p is then determined by a measurement of Δh. By dimensional analysis, it easy to see that
when Δh is measured in meters, the unit on the right-hand side
of (1) is kg m−1 s−2 -i.e., the pascal. The height difference Δh is
about 760 mm at atmospheric pressure. The non-SI unit torr
corresponds to 1 mm of mercury, but is now defined by the relation 1 Torr = 101 325/760 Pa. (In 1954, a standard atmosphere
was defined to be 101 325 Pa.) The primary NIST manometer
is 3 m tall and contains about 230 kg (500 pounds) of mercury.
It takes about a minute for measurements to stabilize when the
pressure is changed, and measurements are sensitive to vibration. The useful low-pressure limit is a few hundred pascals
[6]. Mercury is a neurotoxin and so the goal is to replace this
cumbersome apparatus by a new technology, described below. Until June 2019, NIST had two similar manometers but the
second has been dismantled [7]. The first still serves as NIST's
primary realization of the pascal over a range of pressures of
great interest.

New Ways to Realize the Pascal
Jousten et al. [8] have reviewed promising technologies for realizing the pascal over ranges from ultra-high vacuum (below
10−7 Pa) to pressures much higher than atmospheric. Here, we
focus on replacing the mercury manometer by a technology
that results in a compact package which is easy to replicate,
and which uses the speed of light rather than the density of
liquid mercury to determine pressure. A brief description is
found in [9] and subsequent references.
Starting with the equation of state of an ideal gas:
	

The ratio N/V is the number gas molecules per unit volume. Since N is simply a number, the SI unit of the right-hand
side of (6) is J/m3, which is identical to the pascal. The temperature T of the gas can be measured, but (6) does not yet reveal
a way to measure p using light. The way forward is to see that
N/V is proportional to n - 1, where n is the index of refraction
of the gas [8]. A very rough approximation is:

	

 2 
p = ( n − 1)  0  ( kBT ) ,	(7)
 α 

where ϵ0 is the electric constant whose uncertainty is negligible, and α is the polarizability of the particular gas molecule.
Equation (7) shows that the pressure of a gas is proportional to
the difference of its index of refraction from 1, the index of refraction of vacuum. The full equation for real gases involves
many additional terms (see e.g., [8], [9]).
At a known temperature T, the measurement of any particular pressure p requires a measurement of Δn = n − 1. This is
analogous to the need to measure Δh in a mercury manometer,
once ρHg, g, and T are known. For helium, the needed optical
and other properties have been calculated more accurately
than p can be measured using the full treatment of (7) [8]. A determination of (n − 1) in helium, either directly or indirectly [9],
thus becomes a determination of pressure.
A prototype device to realize the pascal in this way, called
the Fixed-Length Optical Cavity (FLOC), consists of two
Fabry-Perot optical cavities of equal length, produced within
a block of ultra-low expansion glass [8]. The cavity length is
15 cm. As shown in Fig. 3, the ends of both cavities are terminated by silicate-bonded, semi-reflective glass windows. In
Fig. 3, the lower cavity can be evacuated, but the upper cavity has a slot that opens the cavity to the test gas. The FLOC is
housed in a copper enclosure (Fig. 4) to help ensure uniform
temperature.
Laser light in the evacuated cavity will be in resonance
at some frequency, determined by the cavity's length L. The
speed of light is slower in the gas-filled cavity, whose length

pV = N  ( kBT ),	(5)

where p is the pressure of the gas, V is its volume, T is its absolute temperature, N is the number of molecules in the volume,
and kB is the Boltzmann constant. The value of kB has been defined to be exact since May 20, 2019. The unit of kBT is the joule.
Dividing (5) by V yields:
	

12	

p=

N
 ( k T ) .	(6)
V B

Fig. 3. The 15 cm long Fixed-Length Optical Cavity can be held in one hand
(photo credit: NIST).

IEEE Instrumentation & Measurement Magazine	

May 2020



Instrumentation & Measurement Magazine 23-3

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