Athermometer having first-order dynamics with a time constant of 1 min is placed in a temperature bath at 100of. after the thermometer reaches steady state, it is suddenly placed in a bath at 110of at t = 0 and left there for 1 min, after which it is immediately returned to the bath at 100of.(a) plot the variation of the thermometer reading with time (no hand-sketched plot ) calculate the thermometer reading at t = 0.5 min and at t = 2.0 min.

(a) See below

(b) 103.935 °F; 102.235 °F

Explanation:

The equation relating the temperature to time is

1. Calculate the thermometer readings after  0.5 min and 1 min

(a) After 0.5 min

(b) After 1 min

2. Calculate the thermometer reading after 2.0 min

T₀ =106.321 °F

ΔT = 100 - 106.321 °F = -6.321 °F

  t = t - 1, because the cooling starts 1 min late

3. Plot the temperature readings as a function of time.

The graphs are shown below.

c) always accurate

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