A piston fits into a sleeve, so that the pressure from combustion in the reaction chamber is used to push the piston back at a constant rate and do useful work. The movement of the piston is lubricated by oil which has a viscosity η. Recall: The force due to viscosity is given by Fvis = ηAv/d, where A, v, and d are the relevant surface area, relative velocity, and separation.
The piston has a radius r and a length l, and it moves with velocity v. The sleeve has a radius slightly larger than the piston r + Δr, such that Δr is very small compared to r. The pressure in the chamber is Pcham, and the pressure outside the chamber is Pamb.
Which expression gives the magnitude of the work done by the pressure outside the chamber on the piston during the time Δt?