The block diagram of a stirred tank heater control system is as follows:

The range of the temperature transmitter is from 50C to 30C. Under nominal design conditions, the tank operates at 60C, and the inlet temperature is 45C. The controller gain is 4, and the gains of the control valve and I/P converter are Kv = 2.5 and KIP = 1.5 psi/mA, respectively. The time constant of the tank is 5 minutes. When the setpoint is increased from 60C to 65C, the tank temperature gradually rises to a new steady-state value, and the final temperature of the tank is 64C.

a) Find the offset value.

b) Determine the process gain K2.

c) How long does it take to reach the final steady-state value?"