The dynamic relationship between the reactor outlet temperature (T') and the reactor inlet temperature (To') in a chemical reactor is defined by the transfer function given below. Answer the following questions accordingly:

a. What are the values of the gain and time constant?

b. If a step-type 20C increase occurs in the reactor inlet temperature, and the initial steady-state value of the outlet temperature is 90C, what is the new steady-state value?

c. How long will it take for the reactor outlet temperature to return to steady state?