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

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.