Q67PE - College Physics (Urone)

Question

(a) A nuclear power plant converts energy from nuclear fission into electricity with an efficiency of \(35.0\% \). How much mass is destroyed in one year to produce a continuous \(1000{\rm{ }}MW\) of electric power? 

(b) Do you think it would be possible to observe this mass loss if the total mass of the fuel is \({10^4}{\rm{ }}kg\) ?

Step-by-Step Solution

Answer

1. The total mass being destroyed is obtained as:\(1\;kg\).
2. The observation of the mass loss is insignificant.

Step 1: Given Data

The value of total mass of the fuel is:

\({10^4}{\rm{ }}kg\)

The amount of electric power needed to be produced is: \(1000{\rm{ }}MW\).

The efficiency by which the energy is converted from nuclear fission is: \(35.0\% \).

Step 2: Define Special Relativity

The special theory of relativity, sometimes known as special relativity, is a physical theory that describes how space and time interact. Theoretically, this is known as STR theory.

Step 3: Evaluating the mass destroyed

a. Total energy that the power plant will produce in one year is obtained as:

\(\begin{aligned}{E_1} &= (1000MW)\left( {3.15 \times {{10}^7}\;s} \right)\\ & = \left( {1000 \times {{10}^6}\;W} \right)\left( {3.15 \times {{10}^7}\;s} \right)\\ & = 3.15 \times {10^{16}}\;J\end{aligned}\)

As, this is said to be the \(35.0\% \) of the total energy that is produced during mass destruction.

Then, the total energy produced with the help of the mass is obtained as:

\(\begin{aligned}{E_{tot}} & = \dfrac{{{E_1}}}{{35\% }}\\ & = \dfrac{{\left( {3.15 \times {{10}^{16}}\;J} \right)}}{{0.35}}\\ & = 9.00 \times {10^{16}}\;J\end{aligned}\)

So, the total mass that is destroyed is obtained as:

\(\begin{aligned}{m_u} & = \dfrac{{{E_{tot{\rm{ }}}}}}{{{c^2}}}\\ & = \dfrac{{\left( {9.00 \times {{10}^{16}}\;J} \right)}}{{{{\left( {3 \times {{10}^8}\;m/s} \right)}^2}}}\\&  = 1\;kg\end{aligned}\)

Therefore, the mass destroyed is: \(1\;kg\).

Step 4: Explanation for part b

b. As the entire mass of the fuel is\({10^4}\;kg\), and only \(1\;kg\) is destroyed. As a result, the destroyed mass is four orders of magnitude smaller than the entire mass of the fuel. As a result, it is insignificant.

Therefore, the result obtained is negligible.