Page 183 - Mechanical Engineers' Handbook (Volume 2)

172 Temperature and Flow Transducers

V (4kTR dƒ) (1 / 2) (20a)
n
When the current I is measured instead of the voltage, the equivalent model of the noise
n
signal gives the rms current
I (1 / 2)
4kTdƒ
n
R (20b)
is obtained:
On multiplying Eqs. (20a) and (20b), the noise power P n
P 4kT dƒ (21)
n
which is independent of the resistance value and thus is strictly linearly related to the absolute
temperature.
Sophisticated signal extraction techniques are required. This technique is useful mainly
at the temperature extremes (very low and very high) when other sensors fail. The technique
is promising. Results have been reported up to 1000 C with errors less than 0.5% of reading
over a period of several months. 61
Brixy et al. 62 place a high degree of confidence on noise thermometry since ‘‘it is the
only method of contact thermometry that is not affected by the unavoidable changes in the
sensor at high temperatures.’’ They describe the use of noise thermometry as the reference
method in a study to determine the drift characteristics of WRe thermocouples at tempera-
tures up to 2000 C.

7 ACOUSTIC VELOCITY PROBES
The velocity of stress-wave propagation through a gas, liquid, or solid can be used to measure
temperature. In gases and liquids, the acoustic velocity is used (normal stress or pressure-
wave propagation), whereas both normal and shear stress waves have been used in solids.
Two signal-processing techniques are available: detection of resonance and measurement of
the time of travel. These techniques have been used in both gases and solids, as described
by Tasman and Richter. 63
The acoustic velocity in a perfect gas is given by
a RT 1/2
C
p
C v (22)
Where C and C are the specific heats at constant pressure and at constant volume, respec-
p
v
tively, R is the gas constant, and T is the temperature. Shear stress waves are not present in
gases.
The normal stress propagation velocity in a solid (the extensional wave velocity) is
V 1/2
E

ex
D (23)
where E and D are the modulus of elasticity and the density, respectively.
The shear stress propagation velocity in a solid is
V K 1/2
G
sh
D (24)
where K is a shape factor and G and D are the shear modulus and density, respective-
ly. Torsional waves sent down a cylindrical rod are one embodiment of shear waves. The