A large, complex piece of apparatus has built into it a cooling system containing an unknown volume of cooling liquid. It is desired to measure the...

A large, complex piece of apparatus has built into it a cooling system containing an unknown volume of cooling liquid. It is desired to measure the volume of the coolant without draining the lines. To the coolant was added 11.6 mL of methanol whose molecules included atoms of 14C and that had a specific activity of 580 counts per minute per gram (cpm/g), determined using a Geiger counter. The coolant was permitted to circulate to assure complete mixing before a sample was withdrawn that was found to have a specific activity of 29 cpm/g. The density of methanol is 0.792 g/mL, and the density of the coolant is 0.884 g/mL. Based upon this, the volume of coolant in the system in milliliters is calculated to be