Liquid flowing through a heat exchanger (HX) is heated. A bypass stream is provided to control the temperature of the heated exit stream. From the given plumbing options, the one that provides the most effective temperature control for large disturbances while avoiding vaporization in the heat exchanger is

Step 1: Understanding vaporization risk.
If bypassed cold liquid mixes before entering the heat exchanger, the inlet temperature fluctuates, leading to sudden drops in heat-transfer driving force. During disturbances, this may cause overheating in parts of the HX, increasing the chance of vaporization.
Step 2: Identifying the proper configuration.
The safest and most effective arrangement is where the heat exchanger always receives the full stream and the bypass flow mixes only at the outlet. This ensures:
1. Stable HX inlet temperature,
2. Reduced risk of vaporization,
3. Better control authority because the bypassed stream directly manipulates the exit temperature.
Step 3: Selecting the correct option.
Among the options, only Diagram (C) shows the bypass line mixing with the heated stream after the HX. This provides the best temperature control with minimal risk of overheating or vapor formation inside the exchanger.
Final Answer: (C)
In the block diagram shown in the figure, the transfer function $G=\dfrac{K}{(\tau s+1)}$ with $K>0$ and $\tau>0$. The maximum value of $K$ below which the system remains stable is \(\underline{\hspace{2cm}}\) (rounded off to two decimal places).

It is required to control the volume of the contents in the jacketed reactor shown in the figure.
Which one of the following schemes can be used for feedback control?