A 300 L tank full of air needs to be drawn to vacuum using a vacuum...

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A 300 L tank full of air needs to be drawn to vacuum using a vacuum pump. The air can be considered an ideal gas. The molecular weight of air is 29 g/mol. Initially the tank is at atmospheric pressure. The volumetric flow rate at the inlet to the vacuum pump is 30 L/min regardless of pressure. Note that the inlet of the vacuum pump is the material being drawn out of the tank, meaning that the density into the vacuum pump is equal to the density of the material in the tank. The temperature of the air is 20 C and this temperature is maintained throughout the process. a. Derive an expression for P as a function of time. Plot the pressure (atm) as a function of time for this process. Since this is theoretical data obtained using an equation, a continuous curve is appropriate. b. Now assume that there is a slow leak of air into the tank at 0.005 kg/min from the surroundings (a much more realistic scenario). What is the theoretical pressure limit (at infinite time) in this case? Graph the leak scenario on the same graph as part a. Since this is data from an equation, a continuous curve is appropriate. Hint: lump groups of constants and rename them to simplify the expression. Integral table in the homework folder should help with the integral. A 300 L tank full of air needs to be drawn to vacuum using a vacuum pump. The air can be considered an ideal gas. The molecular weight of air is 29 g/mol. Initially the tank is at atmospheric pressure. The volumetric flow rate at the inlet to the vacuum pump is 30 L/min regardless of pressure. Note that the inlet of the vacuum pump is the material being drawn out of the tank, meaning that the density into the vacuum pump is equal to the density of the material in the tank. The temperature of the air is 20 C and this temperature is maintained throughout the process. a. Derive an expression for P as a function of time. Plot the pressure (atm) as a function of time for this process. Since this is theoretical data obtained using an equation, a continuous curve is appropriate. b. Now assume that there is a slow leak of air into the tank at 0.005 kg/min from the surroundings (a much more realistic scenario). What is the theoretical pressure limit (at infinite time) in this case? Graph the leak scenario on the same graph as part a. Since this is data from an equation, a continuous curve is appropriate. Hint: lump groups of constants and rename them to simplify the expression. Integral table in the homework folder should help with the integral.