Hydrogen, to be produced electrolytically, is needed at $40$MPa and $25C.$ Two possibilities must be considered by the ongineers who are designing the plant:

a$.$ Produce hydrogen at $0\mathrm{.}1$MPa and the compress it mechanically to $40$MPa.

b$.$ Pressurize the electrolyzer to $37$MPa and remove the hydrogen at $40$MPa. This assumes that the internal pressure difference between the oxygen and the hydrogen side is $3$MPa and that the oxygen is produced at the environmental pressure of the electrolyzer.

When operating at $0\mathrm{.}1$MPa, the electrolyzer efficiency is $85\%.$ However, when pressurized, its efficiency falls to $80\%.$ The mechanical compressor has $65\%$ efficiency.

a$.$ How much energy is needed to produce $1$ ton of hydrogen in each case? Calculate the energy required to supply the feed water $($only the energy necessary to force the water into the pressurized environment$).$ Use gas constant $R=8314Jmo{l}^{-1}{K}^{-1}$