Problem assessing Lecture $8($solve in week $9).$

$3.(25$ points$)$ An engineer is exploring the possibility of producing drinking water from seawater using the underwater device shown in Figure $1.$ The system uses the difference between the pressure outside the device $($i$.$e$.,$ the ocean$)$ and inside the device $(\backslash ($ p$\_\{$o$\}=1\backslash$mathrm$\{$bar$\}\backslash ))$ to drive pure water across a selective membrane that completely rejects salt, thus producing pure water by reverse osmosis. The ocean and the underwater device are at an equal and constant temperature of $\backslash (25^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

Figure $1$: Underwater desalination device.

a$)$ Write the equation for the thermodynamic condition satisfied if the water in the device and the surrounding seawater attain equilibrium.