- #1

gfd43tg

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## Homework Statement

Exhaust gas at 400°C and 1 bar from internal-combustion engines flows at the rate of 125 mol s-1 into a waste-heat boiler where saturated steam is generated at a pressure of 1,200 kPa. Water enters the boiler at 20°C (T_σ), and the exhaust gases are cooled to within 10°C of the steam temperature. The heat capacity of the exhaust gases is C_P⁄R=3.34+1.12×〖10〗^(-3) T/K. The steam flows into an adiabatic turbine and exhausts at a pressure of 25 kPa. If the turbine efficiency η is 72%,

(a) What is (W_s ) ̇, the power output of the turbine?

(b) What is the thermodynamic efficiency of the boiler/turbine combination?

(c) Determine (S_G ) ̇ for the boiler and for the turbine.

(d) Express (W_lost ) ̇(boiler) and (W_lost ) ̇(turbine) as fractions of |(W_ideal ) ̇|, the ideal work of the process.

## Homework Equations

## The Attempt at a Solution

Right now I am only working on part (a)

For this problem, I have calculated the enthalpy change of the steam both entering and leaving the turbine using the steam table, as well as the enthalpy of the water entering the boiler. I calculated the change in enthalpy from entering the boiler to leaving the boiler, as well as entering the turbine to leaving the turbine.

I was able to calculate a work per unit mass of the turbine, but the question wants a rate of work term that removes the per mass basis. My next thought is to find the mass flow rate of the water. I believe that the enthalpy change of the gas entering and leaving the boiler is equal to the enthalpy change of the water entering and leaving the boiler.

However, on the bottom I am stuck in my calculation because I don't know the temperature of the gas leaving the boiler. This is troubling to me that the problem says that the gas comes to within ''10° C of the steam''. I don't know if that is supposed to help me, I need an exact temperature to calculate the enthalpy change of the gas. So I'm stuck with a mass flow rate of water that is unknown, and a temperature of gas leaving the boiler that is unknown.