A thermocouple Located in a thermowell and connected to a temperature transmitter is used to measure the liquid temperature in a bioreactor. A steady-state calibration of this instrument (transducer) yields the following data:

A process engineer runs a test on the reactor under controlled conditions in which its temperature is changed by +3 ?C/min. The transmitter output was recorded during this test, converted to ?C, and compared with a standard thermometer which is known to be accurate and to have a time constant of 205. The test data are:

For steady-state conditions, the standard thermometer and thermocouple-transmitter outputs are identical Assuming that the transmitter/thermocouple can be modeled by a first-order transfer function, find K and ?.

Temperature, C Measurement, mA 4.0 100 200 300 8.1 11.9 16.1 400 20.0