The thermal chamber transfer function \(C(s) / E(s)=2.5 /(s+1)\) is based on the units of time being minutes.

(a) Modify this transfer function to yield the chamber temperature \(c(t)\) based on seconds.

(b) Verify the result in part (a) by solving for \(c(t)\) with the door closed and the input \(e(t)=4 u(t)\) volts, (i) using the chamber transfer function found in part (a), and (ii) using the transfer function of Fig. P1.6-1. Show that (i) and (ii) yield the same temperature at \(t=1 \mathrm{~min}\).

Fig. P1.6-1

Door To sensor RT circuits Thermistor Thermal chamber 000 (a) Chamber Disturbance d(1) 2.5 s+0.5 Valve Voltage e(1) Steam line Voltage e(1) 2 s+0.5 Temperature, C c(t) Sensor Voltage 0.04 (b)