A temperature bath in which the temperature varies sinusoidally at various frequencies is used to measure the frequency response of a temperature-measuring element B. The apparatus is shown in Fig. P15.2. A standard thermocouple A, for which the time con?stant is 0.1 min for the arrangement shown in the sketch, is placed near the element to be measured. The response of each temperature-measuring element is recorded simultane?ously on a two-channel recorder. The phase lag between the two chart records at different frequencies is shown in the table. From these data, show that it is reasonable to consider element B as a first-order process and calculate the time constant. Describe your method clearly.

HIN B Frequency, cycles/minPhase lag of B behind A, deg 0.1 0.2 0.4 0.8 1.0 1.5 2.0 3.0 4.0 7.1 12.9 21.8 28.2 29.8 26.0 23.6 18.0 14.2