In a laboratory experiment, a unit pulse input of tracer is given to an ideal plug flow reactor operating at steady state with a recycle ratio, $R=1$. The exit age distribution, $E(t)$, of the tracer at the outlet of the reactor is measured. The first four pulses observed at $t_1, t_2, t_3$ and $t_4$ are shown below.

In addition, use the following data and assumptions

• $R$ is defined as ratio of the volume of fluid returned to the entrance of the reactor of the volume leaving the system
• No reaction occurs in the reactor
• Ignore any dead volume in the recycle loop

In the space time of plug flow reactor is $\tau$ seconds, which one of the following is correct?

1. $t_1 = \tau, t_2=2 \tau, t_3 = 3 \tau, t_4=4 \tau \\$
2. $t_1 = \dfrac{\tau}{2}, t_2= \tau, t_3 = \dfrac{3\tau}{2}, t_4=2 \tau \\$
3. $t_1 = \dfrac{\tau}{2}, t_2= \dfrac{\tau}{4}, t_3 = \dfrac{\tau}{8}, t_4=\dfrac{\tau}{16} \\$
4. $t_1 = \dfrac{\tau}{3}, t_2=\dfrac{2 \tau}{3}, t_3 = \tau, t_4=\dfrac{4 \tau}{3}$

Answer: