# Heat engine question

bcjochim07

## Homework Statement

A nuclear power plant generates 2000 MW of heat energy from nuclear reactions in the reactor's core. This energy is usd to boil water and produce high pressure steam at 300 degrees C. The steam spins a turbine, which produces 700 MW of electric power, then the steam is condensed and the water is cooled to 30 degrees before starting the cycle again

a)What is the maximum possible thermal efficiency?
b)What is the plant's actual efficiency?
c) Cooling water from a river flows through the condenser ( the low temperature heat exchanger) at the rate of 1.2 * 10^8 L/hr. If the water enters the condenser at 18 degrees C, what is its exit temperature?

## The Attempt at a Solution

a) Carnot efficiency = 1 - Tc/Th
1- (303K/573K) = .471

b) rate of Wout = 700 MW = 7 * 10^8 J/s
Rate of Qh = 2000MW = 2 * 10^9 J/s

Efficiency = (7*10^8J/s)/(2*10^9J/s)=.35

c) This is the part that I am confused about. I was going to use the formula for heat and set up an equation for heat lost = heat gained, but I don't know the mass of the steam. Is there a formula I'm not thinking of?

bcjochim07
Ok, I just had an idea

rate of work out = rateQh-rateQc
(7.0*10^8)=(2*10^9J/s)-Qc
Qc= 1.3 * 10^9 J/s

and so 1.3 *10^9J/s * 3600s/1.2*10^8kg = 39000J/kg
Q=mcT
39000 = 1kg*4160T
T= 9.3 so the final temp is 27.3 degrees C Is this correct?

Staff Emeritus
Homework Helper
2000 MW of heat is available.
700 MW of that becomes electrical power.
Energy must be conserved, what happens to the remaining energy?

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