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8 February, 03:32

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

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  1. 8 February, 05:52
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    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.
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