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14:54:4 Page 374
8.36 A T-type thermopile is used to measure temperature difference across insulation in the ceiling of a
residence in an energy monitoring program. The temperature difference across the insulation is used
to calculate energy loss through the ceiling from the relationship
Q ¼ kA c DT=L
ð
Þ
where
A c ¼ ceiling area ¼ 15 m
2
k ¼ insulation thermal conductivity À0.4W/m
C
L ¼ insulation thickness ¼ 0.25 m
DT ¼ temperature difference ¼ 5
C
Q ¼ heat loss(W)
The value of the temperature difference is expected to be 5
C, and the thermocouple emf is
measured with an uncertainty of Æ0.04 mV. Determine the required number of thermopile junctions
to yield an uncertainty in Q of Æ5% (95%), assuming the uncertainty in all variables other than DT
may be neglected.
8.37 A T-type thermocouple referenced to 0
C is used to measure the temperature of boiling water. What
is the emf of this circuit at 100
C?
8.38 A T-type thermocouple referenced to 0
C develops an output emf of 1.2 mV. What is the temperature
sensed by the thermocouple?
8.39 A temperature measurement system consists of a digital voltmeter and a T-type thermocouple. The
thermocouple leads are connected directly to the voltmeter, which is placed in an air conditioned
space at 25
C. The output emf from the thermocouple is 10 mV. What is the measuring junction
temperature?
8.40 The result of more than 60 temperature measurements over time during fixed conditions in a furnace
determines
T ¼ 624:7
C with s T ¼ 2:4
C. The engineer suspects a radiation systematic error. The
walls of the furnace are at 400
C, so that the actual temperature in the furnace may be larger than
624.7, but not less. As such, the lower bound of error is 0
C relative to the measured mean value.
Estimate the radiation error in the measurement; assume reasonable values for the heat transfer
parameters. Develop a statement for the true mean temperature with its confidence interval assuming
the systematic errors follow a rectangular distribution with upper bound from your estimate and
lower bound 0
C relative to the measured mean value.
8.41 Flexivity, k, is a property of bimetallic strips that if known allows the radius of curvature to be
calculated directly as
r c ¼
d
2k T 2 À T 1
ð
Þ
where T 2 is the temperature of interest, T 1 is the assembly temperature of the bimetallic strip, and r c
is infinite. If a 3-cm strip is assembled at 25
C, plot the shape of the strip at temperatures of 50
C,
75
C, and 100
C for a k value of 7:3 Â 10
À5 K
À1 .
374 Chapter 8 Temperature Measurements
14:54:4 Page 374
8.36 A T-type thermopile is used to measure temperature difference across insulation in the ceiling of a
residence in an energy monitoring program. The temperature difference across the insulation is used
to calculate energy loss through the ceiling from the relationship
Q ¼ kA c DT=L
ð
Þ
where
A c ¼ ceiling area ¼ 15 m
2
k ¼ insulation thermal conductivity À0.4W/m
C
L ¼ insulation thickness ¼ 0.25 m
DT ¼ temperature difference ¼ 5
C
Q ¼ heat loss(W)
The value of the temperature difference is expected to be 5
C, and the thermocouple emf is
measured with an uncertainty of Æ0.04 mV. Determine the required number of thermopile junctions
to yield an uncertainty in Q of Æ5% (95%), assuming the uncertainty in all variables other than DT
may be neglected.
8.37 A T-type thermocouple referenced to 0
C is used to measure the temperature of boiling water. What
is the emf of this circuit at 100
C?
8.38 A T-type thermocouple referenced to 0
C develops an output emf of 1.2 mV. What is the temperature
sensed by the thermocouple?
8.39 A temperature measurement system consists of a digital voltmeter and a T-type thermocouple. The
thermocouple leads are connected directly to the voltmeter, which is placed in an air conditioned
space at 25
C. The output emf from the thermocouple is 10 mV. What is the measuring junction
temperature?
8.40 The result of more than 60 temperature measurements over time during fixed conditions in a furnace
determines
T ¼ 624:7
C with s T ¼ 2:4
C. The engineer suspects a radiation systematic error. The
walls of the furnace are at 400
C, so that the actual temperature in the furnace may be larger than
624.7, but not less. As such, the lower bound of error is 0
C relative to the measured mean value.
Estimate the radiation error in the measurement; assume reasonable values for the heat transfer
parameters. Develop a statement for the true mean temperature with its confidence interval assuming
the systematic errors follow a rectangular distribution with upper bound from your estimate and
lower bound 0
C relative to the measured mean value.
8.41 Flexivity, k, is a property of bimetallic strips that if known allows the radius of curvature to be
calculated directly as
r c ¼
d
2k T 2 À T 1
ð
Þ
where T 2 is the temperature of interest, T 1 is the assembly temperature of the bimetallic strip, and r c
is infinite. If a 3-cm strip is assembled at 25
C, plot the shape of the strip at temperatures of 50
C,
75
C, and 100
C for a k value of 7:3 Â 10
À5 K
À1 .
374 Chapter 8 Temperature Measurements