E1C08 09/14/2010
14:54:4 Page 367
T
temperature (
)
T 0
reference temperature (
)
T p
probe temperature (
)
T w wall or boundary temperature (
)
T 1 fluid temperature (
)
U
fluid velocity (lt
À1 )
a
temperature coefficient of resistivity (V/
)
a AB Seebeck coefficient
b
material constant for thermistor resistance (
);
constant in polynomial expansion
AB
Peltier coefficient (m l
2
t
À3 A
Àl
)
s
Thomson coefficient (ml
2
t
À3 A
Àl ); StefanBoltzmann constant for radiation (mt
À3 /
(
)
4 )
u
nondimensional temperature
u x
sensitivity index for variable x (uncertainty
analysis)
r e
resistivity (V, l )
d
thermistor dissipation constant (ml
2
t
À3 /
)
e
emissivity
PROBLEMS
8.1 Define and discuss the significance of the following terms, as they apply to temperature and
temperature measurements:
a. temperature scale
b. temperature standards
c. fixed points
d. interpolation
8.2 Fixed temperature points in the International Temperature Scale are phase equilibrium states for a
variety of pure substances. Discuss the conditions necessary within an experimental apparatus to
accurately reproduce these fixed temperature points. How would elevation, weather, and material
purity affect the uncertainty in these fixed points?
8.3 Calculate the resistance of a platinum wire that is 2 m in length and has a diameter of 0.1 cm. The
resistivity of platinum at 25
C is 9.83 Â 10
À6
V-cm. What implications does this result have for the
construction of a resistance thermometer using platinum?
8.4 Plot the resistance of a platinum wire that is 5 m long as a function of wire diameter ranging from 0.1
mm to 2 mm. Estimate the allowable tensile load for the 0.1 mm wire. (Hint: The modulus of
elasticity of platinum is 145 GPa.)
8.5 An RTD forms one arm of a Wheatstone bridge, as shown in Figure 8.38. The RTD is used to measure
a constant temperature, with the bridge operated in a balanced mode. The RTD has a resistance of
25 V at a temperature of 0
C, and a thermal coefficient of resistance, a ¼ 0.003925
C
À1 . The value
of the variable resistance R 1 must be set to 37 V to balance the bridge circuit.
a. Determine the temperature of the RTD.
b. Compare this circuit to the equal-arm bridge in Example 8.2. Which circuit provides the greater
static sensitivity?
8.6 An RTD forms one arm R 4
ð Þ of a Wheatstone bridge, as shown in Figure 8.8. The RTD is used to
measure a constant temperature, with the bridge operated in deflection mode. The RTD has a
resistance of 25 V at a temperature of 0
C, and a thermal coefficient of resistance, a ¼
0.003925
C
À1 . If the RTD is subjected to a temperature of 100
C and the input voltage to the
bridge is 5V, what is the output voltage?
Problems 367
14:54:4 Page 367
T
temperature (
)
T 0
reference temperature (
)
T p
probe temperature (
)
T w wall or boundary temperature (
)
T 1 fluid temperature (
)
U
fluid velocity (lt
À1 )
a
temperature coefficient of resistivity (V/
)
a AB Seebeck coefficient
b
material constant for thermistor resistance (
);
constant in polynomial expansion
AB
Peltier coefficient (m l
2
t
À3 A
Àl
)
s
Thomson coefficient (ml
2
t
À3 A
Àl ); StefanBoltzmann constant for radiation (mt
À3 /
(
)
4 )
u
nondimensional temperature
u x
sensitivity index for variable x (uncertainty
analysis)
r e
resistivity (V, l )
d
thermistor dissipation constant (ml
2
t
À3 /
)
e
emissivity
PROBLEMS
8.1 Define and discuss the significance of the following terms, as they apply to temperature and
temperature measurements:
a. temperature scale
b. temperature standards
c. fixed points
d. interpolation
8.2 Fixed temperature points in the International Temperature Scale are phase equilibrium states for a
variety of pure substances. Discuss the conditions necessary within an experimental apparatus to
accurately reproduce these fixed temperature points. How would elevation, weather, and material
purity affect the uncertainty in these fixed points?
8.3 Calculate the resistance of a platinum wire that is 2 m in length and has a diameter of 0.1 cm. The
resistivity of platinum at 25
C is 9.83 Â 10
À6
V-cm. What implications does this result have for the
construction of a resistance thermometer using platinum?
8.4 Plot the resistance of a platinum wire that is 5 m long as a function of wire diameter ranging from 0.1
mm to 2 mm. Estimate the allowable tensile load for the 0.1 mm wire. (Hint: The modulus of
elasticity of platinum is 145 GPa.)
8.5 An RTD forms one arm of a Wheatstone bridge, as shown in Figure 8.38. The RTD is used to measure
a constant temperature, with the bridge operated in a balanced mode. The RTD has a resistance of
25 V at a temperature of 0
C, and a thermal coefficient of resistance, a ¼ 0.003925
C
À1 . The value
of the variable resistance R 1 must be set to 37 V to balance the bridge circuit.
a. Determine the temperature of the RTD.
b. Compare this circuit to the equal-arm bridge in Example 8.2. Which circuit provides the greater
static sensitivity?
8.6 An RTD forms one arm R 4
ð Þ of a Wheatstone bridge, as shown in Figure 8.8. The RTD is used to
measure a constant temperature, with the bridge operated in deflection mode. The RTD has a
resistance of 25 V at a temperature of 0
C, and a thermal coefficient of resistance, a ¼
0.003925
C
À1 . If the RTD is subjected to a temperature of 100
C and the input voltage to the
bridge is 5V, what is the output voltage?
Problems 367