# instrumentation numerical

by queuetea
Tags: instrumentation, numerical
 P: 8 1. The problem statement, all variables and given/known data Assume that the application of a temperature sensor approximates 1st order conditions. The sensor has a time constant of 5 seconds and is suddenly subjected to a temperature step of 25-200°C. what temperature will be indicated 10 seconds after the process has been initiated? 2. Relevant equations ΔT(t)= ΔTo (exp-t/τ), where ΔT0 is the initial temperature difference, at time t= 0 ΔT is the initial temperature difference, at time t τ= time constant 3. The attempt at a solution i did not get that what does statement temperature step means. and what's ΔT(t) and what's ΔTo in this numerical
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Hello queuetea,

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 Quote by queuetea 1. The problem statement, all variables and given/known data Assume that the application of a temperature sensor approximates 1st order conditions. The sensor has a time constant of 5 seconds and is suddenly subjected to a temperature step of 25-200°C. what temperature will be indicated 10 seconds after the process has been initiated? 2. Relevant equations ΔT(t)= ΔTo (exp-t/τ), where ΔT0 is the initial temperature difference, at time t= 0 ΔT is the initial temperature difference, at time t τ= time constant 3. The attempt at a solution i did not get that what does statement temperature step means.
It means that the true temperature surrounding the sensor changed immediately.

If you want a specific example, imagine this. Suppose you have a temperature sensor that is at room temperature, 25o C. Then you take that temperature sensor and drop it into a vat of boiling oil at 200o C. That is what is meant by the temperature step. The temperature surrounding the sensor instantly changes from 25o C to 200o C.

That said, the output of the sensor does not change instantly. It takes time for the internal structure of the sensor itself to change temperature, as well as any mechanisms involved in registering/displaying this change. The overall time constant, τ, is 5 seconds.
 and what's ΔT(t) and what's ΔTo in this numerical
ΔT0: The sensor's true final temperature minus its true initial temperature.

ΔT(t): The sensor's true final temperature minus the sensor's reading at time t.

Note that both of the above are temperature differences. Before you obtain your final answer, you will have to convert a value back to an absolute temperature.
 P: 8 we will take ΔT(t) =200C. & ΔTo=25C in this numerical??
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## instrumentation numerical

 Quote by queuetea we will take ΔT(t) =200C. & ΔTo=25C in this numerical??
No, those are absolute temperatures. You need to work with temperature differences (at least in the beginning).

I'll give you a step forward. ΔT0 = 200o C - 25o C. You can find ΔT(t) using your formula.
 P: 8 thakyou sir:)

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