- #1
CNC101
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Homework Statement
The graph shows the response of a bare thermocouple
which has been subjected to a step change in temperature from 50°C to
10°C. Assuming that the bare thermocouple behaves as a single transfer
lag system, determine the mathematical relationship between the
temperature (T) and time (t).
Homework Equations
To=Ti*e-(t/τ) Eq1.
OR
f(T)=c*e-(kt) where k= LnT1-LnT2/t1-t2 =Ln5/-20=-0.08047 Eq2.
The Attempt at a Solution
Using Eq2., where t=0 :
50e-0.08047(0)=50
t=20:
50e-0.08047(20)=10
So far so good looking at the graph but for other values of time such as t=6 :
50e-0.08047(6)= 30.85, which doesn't look right on the graph. Have I got the mathematical relationship wrong? Or is my time constant wrong?