It is proposed to build a 1 million kW electric power plant with steam as the wo

Question

It is proposed to build a 1 million kW electric power plant with steam as the working fluid. The condensers are to be cooled with river water at a flow rate of 5 x 108 lbm/hr. The maximum steam temperature will be 1,000oF and the pressure in the condensers will be 1 psi. As an engineering consultant, you are asked to estimate the resulting temperature rise of the river far downstream of the plant. What is your estimate? In the process of estimating this ?T, also calculate the heat transfer in the condensers. Assume a Cp for water of 1 Btu/lbm oR.

Explanation / Answer

1. Carnot efficiency
2. River entering temperature Tin

Then:
1st equation: 1st law expressed in time-derivative form
2nd equation: 2nd law expressed in time-derivative form
Third equation: temperature buildup of river water as function of dm/dt, c and dQ2/dt where dQ2/dt is rate of expelled heat into river, dm/dt = rate of water mass flow, c = water specific heat, J/C-kg.

So: 3 knowns: dW/dt = 1 MW, T1 = 550C, Tin
3 unknowns: dQ1/dt, dQ2/dt, ?T
where dQ1/dt = heat rate into system and ?T = Tout - Tin = temperature rise of river water.

Assume T2, the effective lower temperature in the Carnot cycle, is halfway between Tin and Tout, i.e. T2 = (Tin + Tout)/2.

Finally, you must do some research to find what the typical steam-generated electric plant mechanical efficiency is beyond the Carnot efficiency.

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