Q1. A small room (1000ft3) is perfectly sealed and contains air at 1 atm pressure (absolute). There is a large gas cylinder (100ft3) inside the room that contains butane with an initial pressure of 5atm (absolute). Assume that the valve cylinder started leaking ( at t=0) and the mole flowrate of gas leaving the cylinder is proportional to the difference in pressure between the cylinder and the room. Assume that room air does not diffuse into the cylinder. The room is closed with no ventilation. (a) Write the differential equations that would allow you how to find the cylinder pressure, the room pressure and the model fraction of butane change with time. (b) Explain two reasons for why it is not safe? Using the balance equations, what suggestions do you have to make it safe? (c) Calculate the degree of freedom. Can you have the degree of freedom to be exactly specified