Question

A nuclear power plant generates 3000 MW of heat energy from nuclear reactions in the reactor's core. This energy is used to boil water and produce high-pressure steam at 300?C . The steam spins a turbine, which produces 900MW of electric power, then the steam is condensed and the water is cooled to 25?C before starting the cycle again.

A)

What is the maximum possible thermal efficiency of the power plant?

Express your answer using two significant figures.

B)

Cooling water from a river flows through the condenser (the low-temperature heat exchanger) at the rate of 1.2

Answer 1

a) Max. poss. eta is the Carnot theoretical value 1-Tc/Th = 0.4712.

b) If 3,000 MW are going into the system, and only 900 MW are used, then 2,100 MW should be fed into the cold reservoir. Solving for Joules per second.

2100MW=2.1?10⁶J/s

Solving for volume per second.

1.28?10⁸L/hr?1hr/3,600s?1m³/31,000L=100/3 m³/s

Solving for mass.

(M)kg=(1,000 kg/m³)(100/3 m³/s)=100,000/3 kg/s

Q=Mc?T

2.1?10⁶J=(100,000/3 kg)(4190 J/kg?K)(T_fK?291K)

(2.1?10⁶J)/((100,000/3kg)(4190J/kg?K))+291K=Tf=291.0093K=18.009?C