Final answer:
An "E" size cylinder at 1500 psig and a flow rate of 3L/min holds approximately 906.67 liters of gas and will last around 5.04 hours. The multiple-choice options provided do not match this answer, indicating a potential error in the parameters or need for additional information.
Step-by-step explanation:
To calculate how long an "E" size cylinder with 1500 psig of pressure set at a flow rate of 3L/min will last, first we need to know the total volume of gas in the cylinder at that pressure. The volume of an "E" size cylinder is generally around 680 liters when filled to its service pressure, which is around 2000 psig. So, we would first adjust the volume to reflect the current pressure of 1500 psig.
To do this adjustment, we use the ideal gas law (PV = nRT), but as we're just looking for the ratio of the pressures, we can simplify it to P1V1 = P2V2 since nRT (amount of substance, gas constant, temperature) will be constant for the same gas in the same cylinder just at different pressures.
Let's calculate using the starting pressure P1 = 2000 psig and the current pressure P2 = 1500 psig.
V2 = (P1/P2) × V1
V2 = (2000/1500) × 680 liters
V2 = (4/3) × 680 liters
V2 = 906.67 liters
Now, we can calculate the duration for which the cylinder will last with this volume of gas at 3L/min:
Time = Volume / Flow Rate
Time = 906.67 liters / 3 liters/min
Time = 302.22 minutes
Time in hours = Time in minutes / 60
Time in hours = 302.22 / 60
Time in hours = 5.04 hours
When rounded to the nearest tenths place, the cylinder will last approximately 5.0 hours, which is not an option provided in the multiple choices. Since there could be a mistake in the options given or additional factors not considered (e.g., reserve pressure not used for calculations), it's advisable to double-check the assumptions or potentially seek more information.