$($Elliott P$3\mathrm{.}1)$ Dimethyl ether $($DME$)$ synthesis provides a simple prototype of many petrochemical

processes. Ten tones $(10,000kg)$ per hour of methanol are fed at $25C.$ The entire process operates at

roughly $10$ bar. It is $50\%$ converted to DME and water at $250C.$ The reactor effluent is cooled to $75C$

and sent to a distillation column where $99\%$ of the entering DME exits the top with $1\%$ of the entering

methanol and no water. This DME product stream is cooled to $45C.$ The bottoms of the first column are

sent to a second column where $99\%$ of the entering methanol exits the top at $136C,$ along with all the

DME and $1\%$ of the entering water and is recycled. The bottoms of the second column exit at $179C$ and

are sent for wastewater treatment. Use the method of Example $3\mathrm{.}6($b$)$ in the text to complete the

following:

$($a$)$ Calculate the enthalpy in GJ$/$h of the feed stream of methanol.

$($b$)$ Calculate the enthalpy in GJ$/$h of the stream entering the first distillation column.

$($c$)$ Calculate the enthalpy in GJ$/$h of the DME product stream.

$($d$)$ Calculate the enthalpy in GJ$/$h of the methanol recycle stream.

$($e$)$ Calculate the enthalpy in GJ$/$h of the aqueous product stream.

$($f$)$ Calculate the energy balance in GJ$/$h of the entire process. Does the process involve a net energy

need or surplus? $($ANS$.-50,-106,-26,-51,-31,-7,$ i$.$e$.,$ energy surplus$)$

Thank you for helping. Sorry for such a long question