How much mass is converted into energy per day in Tarapur Nuclear Power Plant operated at 10⁶ kW?

Concept:

• Binding energy (B.E.): The neutrons and protons in a stable nucleus are held together by nuclear forces and energy is needed to pull them infinitely apart (or the same energy is released during the formation of the nucleus). This energy is called the binding energy of the nucleus.
• The binding energy of a nucleus may be defined as the energy equivalent to the mass defect of the nucleus.
• If Δm is a mass defect then according to Einstein's mass-energy relation

Binding energy = Δm c²

Where Δm = mass defect, c = speed of light

(This binding energy is expressed in joule because Δm is measured in kg)

Power = Energy / time

Calculation:

Given: Generated power = 10⁶ kW, c = 3 × 10⁸ m/s

Energy = Power × Time

Energy = (10⁶ × 10³) × (24 × 3600) = 864 × 10¹¹ Joule.

E = Δm c²  

\({\rm{\Delta }}m = \frac{{864\; \times \;{{10}^{11}}}}{{9\; \times \;{{10}^{16}}}}\)

Δm = 96 × 10^-3 kg

Δm = 0.96 gram