A nuclear power reactor has pressurized water at 300ºC . (Higher temperatures are theoretically possible but practically not, due to limitations with materials used in the reactor.) Heat transfer from this water is a complex process (see Figure 15.23). Steam, produced in the steam generator, is

Question

A nuclear power reactor has pressurized water at 300ºC . (Higher temperatures are theoretically possible but practically not, due to limitations with materials used in the reactor.) Heat transfer from this water is a complex process (see Figure 15.23). Steam, produced in the steam generator, is used to drive the turbine-generators. Eventually the steam is condensed to water at 27ºC and then heated again to start the cycle over. Calculate the maximum theoretical efficiency for a heat engine operating between these two temperatures.

Strategy
Since temperatures are given for the hot and cold reservoirs of this heat engine, $E f f_{ C }=1-\frac{T_{ c }}{T_{ h }}$ can be used to calculate the Carnot (maximum theoretical) efficiency. Those temperatures must first be converted to kelvins.

Strategy
Since temperatures are given for the hot and cold reservoirs of this heat engine, [latex]E f f_{ C }=1-\frac{T_{ c }}{T_{ h }}[/latex] can be used to calculate the Carnot (maximum theoretical) efficiency. Those temperatures must first be converted to kelvins.

Accepted Answer

Solution
The hot and cold reservoir temperatures are given as 300ºC and 27.0ºC , respectively. In kelvins, then, [latex]T_{ h }=573 K[/latex], and [latex]T_{ c }=300 K[/latex], so that the maximum efficiency is

[latex]E f f_{ C }=1-\frac{T_{ c }}{T_{ h }}[/latex]. (15.35)

Thus,

[latex]E f f_{ C }=1-\frac{300 K }{573 K }[/latex] (15.36)

= 0.476, or 47.6%.

Discussion
A typical nuclear power station’s actual efficiency is about 35%, a little better than 0.7 times the maximum possible value, a tribute to superior engineering. Electrical power stations fired by coal, oil, and natural gas have greater actual efficiencies (about 42%), because their boilers can reach higher temperatures and pressures. The cold reservoir temperature in any of these power stations is limited by the local environment.
Figure 15.24 shows (a) the exterior of a nuclear power station and (b) the exterior of a coal-fired power station. Both have cooling towers into which water from the condenser enters the tower near the top and is sprayed downward, cooled by evaporation.

Question 15.4: A nuclear power reactor has pressurized water at 300ºC . (Hi...

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