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b. By considering recovery and radiation errors, estimate the possible value for total error in the
indicated temperature. Discuss whether this estimate of the measurement error is conservative,
and why or why not. The heat-transfer coefficient may be taken as 100 W/m
2 K.
8.32 In Example 8.5, an uncertainty value for R T was determined at 125
C as B R T ¼ 247 V (95%). Show
that this value is correct by performing an uncertainty analysis on R T . In addition, determine the value
of B R T at the temperatures 150
C and 100
C. What error is introduced into the uncertainty analysis
for b by using the value of B R T at 125
C?
8.33 The thermocouple circuit shown in Figure 8.43 measures the temperature T 1 . The potentiometer
limits of error are given as:
Limits of error: Æ0.05% (95%) of reading þ15 mV at 25
C
Resolution: 5 mV
Give a best estimate for the temperature T 1 , if the output emf is 9 mV.
8.34 A concentration of salt of 600 ppm in tap water causes a 0.05
C change in the freezing point of water.
For an ice bath prepared using tap water and ice cubes from tap water at a local laboratory and having
1500 ppm of salts, determine the error in the ice-point reference. Upon repeated measurements, is
this error manifested as a systematic or random error? Explain.
8.35 A platinum RTD (a ¼ 0.00392
C
À1 ) is to be calibrated in a fixed-point environment. The probe is
used in a balanced mode with a Wheatstone bridge, as shown in Figure 8.44. The bridge resistances
are known to an uncertainty of Æ0.001 V (95%). At 0
C the bridge balances when R c ¼ 100.000 V.
At 100
C the bridge balances when R c ¼ 139.200 V.
a. Find the RTD resistance corresponding to 0
C and 100
C, and the uncertainty in each value.
b. Calculate the uncertainty in determining a temperature using this RTD–bridge system for a
measured temperature that results in R c ¼ 300 V. Assume u a ¼ Æ1 Â 10
À5 /
C (95%).
Connecting
block
Potentiometer
u
C
e
F
u
C
n
C
T 1
T = 25 0.2 C
T = 21.5
0.2 C
Figure 8.43 Thermocouple circuit
for Problem 8.33.
R c
R a = 100 Ω
R T D
R b = 100 Ω
Figure 8.44 Bridge circuit for Problem 8.35.
Problems 373
14:54:4 Page 373
b. By considering recovery and radiation errors, estimate the possible value for total error in the
indicated temperature. Discuss whether this estimate of the measurement error is conservative,
and why or why not. The heat-transfer coefficient may be taken as 100 W/m
2 K.
8.32 In Example 8.5, an uncertainty value for R T was determined at 125
C as B R T ¼ 247 V (95%). Show
that this value is correct by performing an uncertainty analysis on R T . In addition, determine the value
of B R T at the temperatures 150
C and 100
C. What error is introduced into the uncertainty analysis
for b by using the value of B R T at 125
C?
8.33 The thermocouple circuit shown in Figure 8.43 measures the temperature T 1 . The potentiometer
limits of error are given as:
Limits of error: Æ0.05% (95%) of reading þ15 mV at 25
C
Resolution: 5 mV
Give a best estimate for the temperature T 1 , if the output emf is 9 mV.
8.34 A concentration of salt of 600 ppm in tap water causes a 0.05
C change in the freezing point of water.
For an ice bath prepared using tap water and ice cubes from tap water at a local laboratory and having
1500 ppm of salts, determine the error in the ice-point reference. Upon repeated measurements, is
this error manifested as a systematic or random error? Explain.
8.35 A platinum RTD (a ¼ 0.00392
C
À1 ) is to be calibrated in a fixed-point environment. The probe is
used in a balanced mode with a Wheatstone bridge, as shown in Figure 8.44. The bridge resistances
are known to an uncertainty of Æ0.001 V (95%). At 0
C the bridge balances when R c ¼ 100.000 V.
At 100
C the bridge balances when R c ¼ 139.200 V.
a. Find the RTD resistance corresponding to 0
C and 100
C, and the uncertainty in each value.
b. Calculate the uncertainty in determining a temperature using this RTD–bridge system for a
measured temperature that results in R c ¼ 300 V. Assume u a ¼ Æ1 Â 10
À5 /
C (95%).
Connecting
block
Potentiometer
u
C
e
F
u
C
n
C
T 1
T = 25 0.2 C
T = 21.5
0.2 C
Figure 8.43 Thermocouple circuit
for Problem 8.33.
R c
R a = 100 Ω
R T D
R b = 100 Ω
Figure 8.44 Bridge circuit for Problem 8.35.
Problems 373