4-31 The temperature of a gas stream is to be measured by a thermocouple whose junction can be approximated as a 1.2-mm-diameter sphere. The properties of the junction are k 35 W/m K, p = 8500kg/m3, and c, = 320 J/kg-K, and the heat transfer coefficient between the junction and the gas is h = 110 W/m2-K. Determine how long it will take for the thermocouple to read 99 percent of the initialtemperature difference.Answer: 22.8 s

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Asked Oct 22, 2019
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4-31 The temperature of a gas stream is to be measured by a thermocouple whose junction can be approximated as a 1.2-mm-diameter sphere. The properties of the junction are k 35 W/m K, p = 8500
kg/m3, and c, = 320 J/kg-K, and the heat transfer coefficient between the junction and the gas is h = 110 W/m2-K. Determine how long it will take for the thermocouple to read 99 percent of the initial
temperature difference.
Answer: 22.8 s
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4-31 The temperature of a gas stream is to be measured by a thermocouple whose junction can be approximated as a 1.2-mm-diameter sphere. The properties of the junction are k 35 W/m K, p = 8500 kg/m3, and c, = 320 J/kg-K, and the heat transfer coefficient between the junction and the gas is h = 110 W/m2-K. Determine how long it will take for the thermocouple to read 99 percent of the initial temperature difference. Answer: 22.8 s

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Expert Answer

Step 1

The characteristics length of the thermocouple is,

V
Lc
Acuface
6
D
6
0.0002 m
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V Lc Acuface 6 D 6 0.0002 m

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Step 2

The Biot number for the thermocouple sphere is,

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Step 3

The Biot number of the sphere is less than <0.1. Thu...

From the expression of lumped bodies,
TO) -т,
Т -Т.
Here, b is time constant
bt
The expression for the time constant b is,
b =
pLC
(110 W/m2 .K)
b =
(8500 kg m')(0.0002 m) (320 J/kg K)
b 0.2
help_outline

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From the expression of lumped bodies, TO) -т, Т -Т. Here, b is time constant bt The expression for the time constant b is, b = pLC (110 W/m2 .K) b = (8500 kg m')(0.0002 m) (320 J/kg K) b 0.2

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