A nuclear-fueled electric power plant utilizes a so-called \"boiling water react

Question

A nuclear-fueled electric power plant utilizes a so-called "boiling water reactor." In this type of reactor, nuclear energy causes water under pressure to boil at 312° C (the temperature of the hot reservoir). After the steam does the work of turning the turbine of an electric generator, the steam is converted back into water in a condenser at 41° C (the temperature of the cold reservoir). To keep the condenser at 41° C, the rejected heat must be carried away by some means-for example, by water from a river. The plant operates at three-fourths of its Carnot efficiency, and the electrical output power of the plant is 1.19x10^9 watts. A river with a water flow rate of 9.10 x10^4 kg/s is available to remove the rejected heat from the plant. Find the number of Celsius degrees by which the temperature of the river rises.

? C°

Explanation / Answer

higher temp T = 312 oC = 312 + 273 = 585 K lower temp T ' = 41 oC = 41 + 273 = 314 K efficiency of the carnot engine n = 1-( T ' / T )                                                  = 0.4632 efficiency of the plant n ' = ( 3/ 4) n = 0.3474 the electrical output power of the plant P= 1.19x10^9 watts water flow rate m = 9.10 x10^4 kg/s the number of Celsius degrees by which the temperature of the river rises t =? we know n ' = P / Q from htis heat taken Q = P / n'                                     = 3.425*10^9 J / s heat removed Q ' = Q - P = 2.235* 10^9 J / s we know Q ' = m C dt from this temperature raise dt = Q ' / mC    where C = Specific heat of water = 4186 J / kg oc                                               = 5.86 oC

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