An insulated sphere contains two hemispheres A and B. Each section contains a monatomic ideal gas. The sections are separated by an insulating perfectly flexible wall. Initially the pressure is the same on both sides (85 kPa) and the volumes are the same (1 m3). Heat is supplied to gas B by means of an electrical resistance (a hot wire) until the pressure increases by a factor of 3. If the perfectly flexible wall allows both gases to maintain equal pressures and the initial temperature of both gases is 273 K, compute: (10 points)

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