A nuclear power plant operates near the ocean, where water temperatures average

Question

A nuclear power plant operates near the ocean, where water temperatures average 14° C. The power plant creates superheated steam at 1162° C for driving turbines to create electricity. The power plant operates at exactly half its ideal carnot efficiency and uses 1500MW of thermal energy from its fuel.

A. What is the power output of the power plant in MW?

B. For a hydroeelctric plant to generate the same power from 1,000,000 kg of falling water per second, how many meters high would the dam have to be?

Explanation / Answer

a) hot temperature=1162+273=1435 K

cold temperature=273+14=287 K

then carnot efficiency=1-(cold temperature/hot temperature)

=1-(287/1435)

=0.8

given that efficiency of the plant is half of the ideal efficiency

hence efficiency of the plant=0.8/2=0.4

as we know, efficiency=output/input

==>0.4=output/1500

==>output=1500*0.4 MW=600 MW

hence output of the power plant is 600 MW

part b:

if height of the dam be h,

then mass of water falling per second*9.8*h=power

==>1000000*9.8*h=600*10^6

==>h=600/9.8=61.224 m

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