• Support PF! Buy your school textbooks, materials and every day products Here!

Instrumentation numerical

  • Thread starter queuetea
  • Start date
  • #1
8
0
1. Homework Statement

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. Homework 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
 

Answers and Replies

  • #2
collinsmark
Homework Helper
Gold Member
2,853
1,176
Hello queuetea,

Welcome to Physics Forums!
1. Homework Statement

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. Homework 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.
 
  • #3
8
0
we will take ΔT(t) =200C. & ΔTo=25C in this numerical??
 
  • #4
collinsmark
Homework Helper
Gold Member
2,853
1,176
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.
 
  • #5
8
0
thakyou sir:)
 

Related Threads for: Instrumentation numerical

  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
954
  • Last Post
Replies
8
Views
362
  • Last Post
Replies
5
Views
3K
Top