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A nuclear power plant generates 3000MWof heat energy from nuclear reactions in the reactor鈥檚 core. This energy is used to boil water and produce high-pressure steam at 300C. The steam spins a turbine, which produces 1000MWof electric power, then the steam is condensed and the water is cooled to 25Cbefore starting the cycle again.

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

b. What is the plant鈥檚 actual efficiency?

c. Cooling water from a river flows through the condenser (the low-temperature heat exchanger) at the rate of 1.2*108L/h ( 30 million gallons per hour). If the river water enters the condenser at 18C, what is its exit temperature?

Short Answer

Expert verified

(a) Thermal efficiency48%

(b) Plant's actual efficiency33%

(c) Temperature of exit is 320C

Step by step solution

01

Find Thermal Efficiency (part a)

If the thermal cycle is of the Carnot type, the maximum efficiency can be achieved. It will be Thand Tcif the working temperatures are Thand Tc.

=1-TcTh=Th-TcTh

It is numerically be in our instance.

=300-25300+273=48%

02

Find Plant's Efficiency (part b)

The real efficiency is simply,

=PePh=10003000=33%
03

Find Temperature (part c)

It is self-evident that heat dumped to cold source can be calculated as follows.

Pc=Ph-Pe=2000MW= 2109J/s

This heat is absorbed by flowing river water , due to which there is rise in its temperature .

If the temperature difference is T, the heat taken from mass mof water is given by

Q=cmT

When we divide the mass by the volume and density of the mass, we get

Q=cVT

Let's divide the time on both sides now. On the left, we'll get the cooling power, and on the right, we'll divide the volume to get the volumetric flow rate.

Pc=cVtT

It is evident that the temperature difference can be expressed as

T=PctcV

If the temperature at the input is Ti, the temperature at the output will obviously be To.

Apply the values,

localid="1649656479751" To=18+21093600418010001.2105=32C

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