Question 3 (25 points) A cast iron natural gas pipeline in Boston has 115 kg of natural gas. However, this century old gas line has suddenly sprung a leak! Prior to the leak, the natural gas sits in the pipeline at a pressure of 100 psi (pounds per square inch). The volume of the pipe is 20 m³ and the molar mass of natural gas is 19.0 g/mol. a) (5 points) Calculate the initial temperature in the pipeline (assume natural gas is ideal) b) (5 points) 1 hour after the pipeline has started leaking, the pressure has dropped to 50 psi. Calculate the percentage of gas lost in 1 hour. Assume natural gas is an ideal gas and an isothermal leak. Now we will perform the same calculations, but without the ideal gas law assumption. Since we do not know the van der Waals constants for natural gas at these conditions, try two different sets of constants to see the impact of a and b on the temperature and amount of gas lost. Again, assume an isothermal leak. SET 1: a = 0.15 L2bar/mol², b = 0.005 L/mol SET 2: a = 1.35 L2bar/mol², b = 0.013 L/mol c) (5 points) Calculate the temperature in the pipeline with the van der Waals constants SET 1. Report the % error in this temperature calculation relative to the ideal gas calculation. d) (5 points) Calculate the temperature in the pipeline with the van der Waals constants SET 2. Report the % error in this temperature calculation relative to the ideal gas calculation. e) (5 points) What is the impact of increasing the a and b van der Waals constants? Conceptually explain in your own words. f) (Extra Credit: 10 points) Calculate the amount of gas lost in 1 hour, for van der Waals constants SET 1 and SET 2. Report the amount of gas lost and % error, relative to the ideal gas calculation in b.