When the bombardier beetle is attacked or provoked, it sprays a jet of hot liquid toward its attacker. The jet comes out of an opening at the tip of its abdomen, which it can move in order to direct the stream.
The physical mechanism for creating the hot spray consists of two chambers in the abdomen: an inner chamber which stores hydrogen peroxide and hydroquinone in water solution, connected by a valve to an outer chamber which contains oxidative enzymes (peroxidase and catalase) adhered to the walls. The beetle squeezes the hydrogen peroxide and hydroquinone into the outer chamber where the following reaction takes place to form quinone (also called 1,4-benzoquinone):
The heats of formation of the various compounds are shown in the table.
hydrogen peroxide –45.68
This reaction in the outer chamber creates a solution of the products of reaction (1) in water. This solution has enough heat and pressure to create a hot stream to shoot out of an opening (radius 0.1 mm) in the tip of the abdomen at a speed v = 12 m/s.
We can model this outer chamber as a volume (reaction flask) with a nozzle. The pressure in the chamber Pcham is greater than the outside pressure Patm, and this provides the force on the fluid in the nozzle. The nozzle has radius r and cross-sectional area A, and the entire chamber has volume Vcham. The temperature of the fluid in the chamber is Tcham.
In reference to the model in the last paragraph, which gives the best expression for the total force on the part of the fluid in the nozzle?