To solve this problem, we will use the conservation of mass and energy, as well as the definition of exergy and second-law efficiency.
a. The temperature of saturated steam entering the chamber can be found by using the steam tables. At the pressure of the steam entering the chamber, which is not given in the problem, the saturation temperature is slightly above 100°C. Since the mixture leaves the chamber as a liquid at 45°C, we can assume that the steam is also at 45°C, which is the final temperature of the mixture. Therefore, the temperature of the saturated steam entering the chamber is 45°C.
b. The exergy destruction during this mixing process can be calculated as the difference between the inlet exergy and the outlet exergy of the system. The inlet exergy can be calculated as the sum of the exergy of the liquid water and the exergy of the saturated steam, which are both at the same temperature of 45°C. The outlet exergy can be calculated as the exergy of the liquid water at 45°C, assuming that there is no exergy transfer to the surroundings. The exergy destruction is then:
ΔE = (m_water * e_water + m_steam * e_steam) - m_outlet * e_outlet
where m_water and m_steam are the mass flow rates of the liquid water and saturated steam, respectively, and e_water, e_steam, and e_outlet are the specific exergies of the liquid water, saturated steam, and outlet liquid water, respectively.
Using the steam tables, we can find that the specific exergies of the liquid water and saturated steam at 45°C are 199.23 kJ/kg and 2513.9 kJ/kg, respectively. Therefore, the exergy destruction is:
ΔE = (4.6 kg/s * 199.23 kJ/kg + 0.19 kg/s * 2513.9 kJ/kg) - 4.79 kg/s * 199.23 kJ/kg
ΔE = 6253.7 kW
c. The second-law efficiency of the mixing chamber can be defined as the ratio of the actual work output (which is zero in this case) to the maximum possible work output, which is the inlet exergy minus the exergy destruction. Therefore, the second-law efficiency is:
η_II = 0 / (m_water * e_water + m_steam * e_steam - ΔE)
η_II = 0 / (4.6 kg/s * 199.23 kJ/kg + 0.19 kg/s * 2513.9 kJ/kg - 6253.7 kW)
η_II = 0
This means that the mixing process is not reversible, and there is no useful work output.