Chapter 36: Q. 67 (page 1062)

A typical nuclear power plant generates electricity at the rate of $1000 MW$ . The efficiency of transforming thermal energy into electrical energy is $\frac{1}{3}$ and the plant runs at full capacity for $80 %$ of the year. (Nuclear power plants are down about $20 %$ of the time for maintenance and refueling.)
a. How much thermal energy does the plant generate in one year?
b. What mass of uranium is transformed into energy in one year?

Expert verified

a. The thermal energy garneted is $2.52 \times 10^{15} J .$

b. Mass of uranium is $0.083 kg .$

Step by step solution

We have given,

power generates = $1000 MW$

We have to find the thermal energy generated by the plant.

In one year the seconds = $60 \times 60 \times 24 \times 365 = 31536000 s$

then using the relation between power and energy we can write,

$E = Pt E = 1000 \times 10^{6} W \times 31536000 s E = 2.52 \times 10^{15} J$

we have given,

Efficiency = $\frac{1}{3}$

capacity = $80 %$

we have to find the mass of uranium.

since,

$E = {mc}^{2} m = \frac{E}{c^{2}} m = \frac{2.52 \times 10^{15} J}{{(3 \times 10^{8} m / s)}^{2}} m = 0.083 kg$

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