An electrically heated process is known to exhibit second-order dynamics with the following parameter values K is 3 °C/kW, τ = 3 mm, ε = 0.7. If the process initially is at steady state at 70 °C with heater input of 20 kW and the heater input is suddenly changed to 26 kV and held there:

(a) What will be the expression for the process temperature as a function of time?

(b) What will be the maximum temperature that one observes? When will it occur?