A jacketed vessel similar to the one in Exercise 2.8 is used to heat a liquid by means of condensing steam. The following information is available:

(i) The volume of liquid within the tank may vary.

(ii) Heat losses are negligible.

(iii) The tank contents are well mixed. Steam condensate is removed from the jacket by a steam trap as soon as it has formed.

(iv) Thermal capacitances of the tank and jacket walls are negligible.

(v) The steam condensation pressure Ps is set by a control valve and is lot necessarily constant.

(vi) The overall heat transfer coefficient U for this system is constant.

(vii) Flow rates q’ and q are independently set by external valves and may vary.

Derive a dynamic model for this process. The model should be simplified as much as possible. State any additional assumptions that you make.