Consider 0.25 mol ideal gas initially at pressure 2 bar, placed in a hot water bath held 290k. suppose that a latch in the container is released at fixed temperature t allowing it to expand by av 0.5 liters against external pressure. evaluate the heat flow into the system, the work done on the system, and the system's change in internal energy for (10 points) pert = 0.8 bar and (10 points) pet = 0 bar (vacuum) (2) (10 points) for the system in problem 1, determine the maximum amount of work that the gas can do on its environment, when expanding by av 0.5 liters at fixed temperature t = 290 k. (3) (10 points) repeat problem 2 for the case where the hot water bath is replaced with an adiabatic container, such that no heat can flow between the system and the envi ronment. assume the initial temperature is 290 k