I think that's what the question is trying to tell us , that is that the work done to the gas is ##n2\pi l F## and since the chamber is thermally isolated and we assume the transfer to be instantaneous ##\Delta U+W=0## and from this to calculate the ##\Delta T## to answer perhaps e). But yes since it says the piston is fixed, don't know what crank is that that does work to the system. Also instantaneous transfer that takes n turns of a crank doesn't seem too orthological either...(2) This might be a garbled version of a similar question that I have come across before . In that there was a screw being driven by the crank and the action of the screw propelled the piston down through a cylinder . N turns of the screw with a known applied torque gave a value for work done .