Avertical piston-cylinder assembly containing a gas is placed on a hot plate. the piston initially rests on stops and has a mass of 50 kg, while atmospheric pressure is patm = 101.325 kpa. let the area of the piston be a = 0.01 m2 and assume that gravity is g = 9.81 m/s2 . a) (5 pts) at what pressure, in kpa, will the piston begin to rise? b) (5 pts) assume the piston rises 10 cm. if the amount of work done by the gas equals the change in total energy of the piston, how much work has been done, in j?

Asquare 1m x 1m plate is shown below. all four of its edges are kept at 0 co. at t=0the temperature distribution is given by: y xtsins n75)=.a) using separation of variables determine the temperature distribution t(x,y,t)along the plate at any time t.b) discretize the heat conduction equation +=22222 txtusing a second-order centered difference scheme for the two second derivatives and a first-order forward euler scheme for the first derivative. using von neumann stability analysis, determine the stability criterion for the proposed discretization scheme in terms of , hand t. solve for the maximum allowable time step tmax