A reactor is to be designed for the oxidation of sulfur dioxide, with excess oxygen from air, to sulfur trioxide. The entering feed, at \(550 \mathrm{~K}\) and \(1.1 \mathrm{bar}\), consists of \(0.219 \mathrm{kmol} / \mathrm{s}\) of nitrogen, \(0.058 \mathrm{kmol} / \mathrm{s}\) of oxygen, and \(0.028 \mathrm{kmol} / \mathrm{s}\) of sulfur dioxide. The fractional conversion of sulfur dioxide is \(50 \%\). The reaction is very exothermic. Three cases are to be considered:

(a) Adiabatic reaction

(b) Isothermal reaction with the heat of reaction transferred to boiler feed water at \(100^{\circ} \mathrm{C}\)

(c) Isothermal reaction with the heat of reaction transferred to boiler feed water at \(200^{\circ} \mathrm{C}\)

For each case, compute the lost work in \(\mathrm{kW}\).