Question

How much mass is converted into energy per day in the Tarapur nuclear power plant operated at ${{10}^{7\text{ }}}KW$ ?

Answer 1

We know that the nuclear power plant, we should know that a nuclear power plant can be defined as a thermal power station in which a nuclear reactor is used as the main heat source. After that, the heat produced by nuclear reactors is used for generating steam. This steam moves the steam turbines that are connected to generators. And these generators produce the needed electricity.

Complete answer:
Considering the term binding energy, it denotes the energy that is essential to bind two entities. Here, the nature of the two entities is defined by the fact that these two terms are from a nuclear physics background. When we measure the weight of an atomic nucleus, it is observed that the measured weight will always be slightly less than that of the calculated weight which is obtained by the sum of masses of all protons and neutrons present in the nucleus. This difference in the observed and theoretical weights is known as the mass defect.
Here we have $P=107\text{ }KW=\text{ }{{10}^{10}}\text{ }W={{10}^{10}}\text{ }J/s$ Thus, energy produced per day is given as;
${{10}^{10}}\times 24\times 60\times 60=24\times 36\times {{10}^{12}}$ [Here we have use $24\times 60\times 60$ is converting hours into minute into seconds]
As, we know that $E=m{{c}^{2}}.$
Thus, by substituting we get
$24\times 36\times {{10}^{12}}=m{{\left( 3\times {{10}^{8}} \right)}^{2}}$
On further solving we get;
$m=\dfrac{24\times 36\times {{10}^{12}}}{9\times {{10}^{16}}}=2.4\times 4\times {{10}^{-4}}Kg.$
Thus, we get; $m=9.6\times {{10}^{-4}}Kg=96\times {{10}^{-1}}g$
Therefore, the mass is converted into energy per day in Tarapur nuclear power plant operated at ${{10}^{7\text{ }}}KW$ is $9.6g$

Additional Information:
These terms are said to be related in a way that the mass defect is considered to be the binding energy. The difference in the observed weight and the calculated weight is accounted for by the binding energy. It is a bit hard to instinctively predict how energy having mass works. So we use the following formula to facilitate the conversion: $E=m{{c}^{2}}.$ This formula is used to calculate the binding energy of each nucleus using the mass defect as they are seen to be equivalent. Einstein proved that this conversion is possible in his special theory of relativity.

Note:
Remember that the binding energy of the products is always greater than the binding energy of the reactants, and the difference between them is released as energy. Thus, from the above discussion, we can conclude that the binding energy of reactants, when compared with that of products in a nuclear reaction, is always less.