Carbon dioxide has many industrial uses including food and beverage, fire extinguishers,

pharmaceuticals, and research. Instead of allowing the carbon dioxide produced from beer

fermentation to be released to the atmosphere, it can be captured and pressurized and

stored as a liquid under pressure. Due to the large density difference between liquid and

gaseous CO$2$ the liquid form is much easier to store and transport for use in other industrial

applications. One large scale fermentation tank holds about $15,850$ gallons $(600$ hL$)$ of

beer during the fermentation process, which lasts about $3$ weeks on average. On average,

$0\mathrm{.}41$ kg of CO$2$ is produced for every liter of beer. You are tasked with determining the

production rate for filling CO$2$ cylinders $($cylinders$/$h$)$ for one fermenter. Since the CO$2$ is

produced as an off gas, you need to determine:

a$.$ The volumetric flow rate $($L$/$h$)$ that will feed the compressor$/$cooling$/$distillation system

that will liquify the CO$2$ and enable filling the gas which holds $50$ lbs$.$ net weight of liquid

CO$2.$ The fermentation process operates at $20$C and $1$ Atm and the density of liquid

CO$2$ is about $0\mathrm{.}827$ g$/$ml$.$

b$.$ The number of cylinders that can be filled per hour while the fermentation process is

running.