Download Thermometry - Texas A&M University

Bimetallic Thermograph
• Bourdon Thermometer
– Flattened, curved tube filled with organic
liquid.
– Tends to straighten when temperature rises.
– Large hysteresis error compared to other
thermometers
– Slow time response.
ds  LB(Y)(  I   m )dT
• ds = deflection of tube
• L = length of tube at T0
• Y = curvature of tube
• B(Y) = Function of
curvature
• l = Coeff. of cubical
expansion of liquid
• m = Coeff. of cubical
expansion of metal
B. ELECTRICAL THERMOMETERS
• 1. Resistance Type - Resistance, thus
current, changes as temperature changes.
– Positive Resistance Type
– Negative Resistance Type
• Thermistor
• Transistors
– Diodes
• 2. Thermocouple Type - Electrical current
/ voltage changes as a function of a
difference in temperature.
• 3. Radiation Type (measure / sensing of
radiation emitted by object is used to
determine surface temperature of the
emitting object.
– Infrared Thermometer Type
– Brightness Thermometer Type
Positive Resistance Type
Thermometer (PRT)
• Most metals exhibit positive resistance
change to an increase in temperature.
• Platinum is found to be best.
– Advantages
• Higher accuracy
• Higher sensitivity
• Durable
• Corrosion resistant
• Only slightly non-linear across the range of
meteorological temperatures
– Disadvantages
• More expensive
• Wire easily broken with rough use.
• Current must be kept small to prevent wind
effects.
– Accuracy: ±0.25oC at 0oC
– Other metals used: Nickel, copper,
constantan (60% Cu, 40% Ni), Manganin,
Nichrone
– Sensor is typically one arm of a Wheatstone
Bridge
• The PRT transfer equation is typically given
by: RT  R0[1  a (T  T0 )  b (T  T0 )2 ]
• where;
• R0 = Resistance at T0, typically OoC,
• a = First order temperature coefficient
• b = Second order temperature coefficient
• To = Calibration temperature, typically 0oC
• RT = Resistance of sensor at unknown
temperature
• Additional calibration temperatures may be
used for more accurate work.
• Standard calibration temp. is 0oC
• Also, 100oC, -78.51oC, and -182.97oC may
be used.
• Additional terms may be required in the
transfer equation.
Voltage Divider Circuit
• Output voltage is half
the input voltage at
calibration temperature.
• Output voltage changes
as temperature changes.
Bridge Circuits
• A bridge circuit is a special type of circuit
that allows one to compare unknown
resistance against standard (known)
resistances.
• A Bridge circuit is essentially a pair of
voltage divider circuits
• V1 is created by voltage divider RA, RX.
• V2 is created by
voltage divider RB, RC.
• If we measure V1
and V2 and know
RA, RB, and RC, we
can determine RX.
• The resistance of
RX is proportional to temperature by the
PRT transfer equation, thus we can
determine the temperature at Rx.
Bridge Circuit
• The difference in
Vout  V3  GV1  V2 
voltage between V1 and
 V R

V2 is measured and
V
V 3  G in T  in 

amplified because it is
2 
R0  RT

usually quite small.
• The term, G, represents
the amount of
amplification of V1 and
V2 to produce V3.
Negative Resistance
Thermometers (Thermistors)
• Ceramic-like semiconductors
• Constructed of metallic oxides
• Non-linear, negative coefficient of
resistance
• Have rapid time response ~few sec. to 0.1
sec.
RT   RatT  298.16 o K e
0
• The amount of current
flow in a circuit is a
function of the resistance
of the circuit and the
resistance of a thermistor
is a function solely of its
absolute (oK) temperature.
  1 1
b  


  T T 0
 
 
 
 
• Construction of
the thermistor
determines R at
25oC (298.16oK)
• Type of material
determines I/O
curve type.
• A type Y curve for
a thermistor with
R25 = 5000 W
Transistor Temperature Sensors
•
•
•
•
Doped simiconductors in combination
Gallium + germanium produces p-type.
Arsenic + germanium produces n-type.
When collector-emitter voltage is held
constant, the base-emitter voltage is a
function of temperature.
• Accuracy: within ~0.05oC
• Response time: ~5 msec
• This circuit overcomes
some of the problems
of non-linearity. The
difference in BaseEmitter voltage of the
two transistors is a
linear function of
temperature.
V BE  V BE1  V BE2
kT J E1 

ln
q
JE 2
•
•
•
•
Where,
K=Boltzman Constant
q=electron charge
JE1, JE2 = Emitter
current densities
Typical Input/Output Diagram
• The collector to base current, Icb, of many
different silicon transistors have the following
dependence on emitter-base voltage, Veb:
Icb  Icbo (T )  expbV eb   1
• Icbo(T) = a constant determined from
calibration at absolute temperature (T),
q
• b = kT , where q is the electronic charge and
k is the Boltzmann’s constant.
• Transistor temperature sensors are:
– linear,
– negative response,
– accurate to within 0.5oC
• They can be placed at significant distance
from the recorder or indicator equipment with
little effect on the output.
• Normally they are placed inside a protective
shell or coated to protect them from the
elements.
• Operating voltage and current are kept small to
prevent heating of the sensor by the current.