As shown in Fig. P13.90, coal with a mass analysis of 88%

Chapter 13, Problem 13.90

(choose chapter or problem)

As shown in Fig. P13.90, coal with a mass analysis of 88% C, 6% H, 4% O, 1% N, 1% S enters a reactor where it burns with the theoretical amount of air to give a gas stream consisting of \(\mathrm{CO}_{2}\), \(\mathrm{H}_{2} \mathrm{O}\), \(\mathrm{N}_{2}\), \(\mathrm{SO}_{2}\). After the gas stream provides heating in an industrial furnace, it is directed at \(25^{\circ} \mathrm{C}\), 1 atm to a cleanup device operating at steady state that removes the \(\mathrm{CO}_{2}\) and \(\mathrm{SO}_{2}\), each in a separate stream. The remainder is discharged to the atmosphere. Each of these three streams exits the device at \(25^{\circ} \mathrm{C}\), 1 atm, heat transfer to the surroundings occurs at \(25^{\circ} \mathrm{C}\), and the effects of kinetic and potential energy are negligible. Determine the minimum theoretical work input required by any such cleanup device, in kJ per kg of coal entering the reactor. Why is a work input required?