Question

A thermocouple element when taken from a liquid at 50°C and plunged into a liquid at 100° C at time t = 0 gave the following e.m.f. values. Determine the 95% response time. Use linear interpolation inside the intervals

Answer 1

Answer:

t(@95%) = 75 s

Explanation:

Given:

Time (s)         0          20           40           60            80            100            120

emf  (mV)     2.5        3.8          4.5          4.8           4.9             5.0            5.0

Find:

95 % response time t?

Solution:

To formulate the 95% response time t we need to compute the 95% emf value:

                             emf = emf_o + 0.95*(emf_ss - emf_o)

where,

                              emf_o = 2.5 mV and emf_ss = 5.0 V

                              emf = 2.5 + 0.95*(5.0 - 2.5)

                              emf = 4.875 mV @ 95%

We can see that the 95% response lies in the range of 60 s < t < 80. To determine the time for this response we use interpolation for the above interval:

                              t = m*emf + C          (linear interpolation)

where,

                              m:slope and C: t intercept are constants

                              m = ( 80 - 60 ) / (4.9 - 4.8 ) = 200

                              C = 80 - 200*4.9 = -900 s

                              t(4.875) = 200*4.875 - 900

                               t(@95%) = 75 s

Answer: The time taken to reach 95% of the response is t = 75 s.