Question

Multiple-Concept Example 6 reveiws the principles that play a role in this problem. A nuclear power reactor generates 2.3 x 109 W of power. In one year (365.25 days), what is the change in the mass of the nuclear fuel due to the energy being taken from the reactor?

Answer 1

The change in the mass of the nuclear fuel due to the energy being taken from the reactor is 0.81 kg

Step-by-step explanation:

Given:

P = power 2.3x10⁹W

The energy taking from the reactor is:

E = P * t = 2.3x10⁹ * 365 * 24 * 60 * 60 = 7.25x10¹⁶J

The change in the mass is:

E = Δm * c²

Where c is speed of light in vacuum

Δm = E/c² = 7.25x10¹⁶/(3x10⁸)² = 0.81 kg

Answer 2

change in mass = 2.41*10^{8}kg

Step-by-step explanation:

The change in the mass can be computed by using the relation

`E=\Delta mc^2\\\Delta m=(E)/(c^2)`(1)

That is, the energy liberated comes from the mass of the nuclear fuel. The energy generated in one year is

`E=Pt=2.3*10^(9)(J)/(s)*1 year*(365.25 day)/(1 year)*(24h)/(1 day)*(3600s)/(1h)=7.25*10^(16)J`

Hence, by replacing in the equation (1) you have (c=3*10^{8}m/s)

`\Delta m=(7.25*10^(16)J)/(3*10^(8)(m)/(s))=2.41*10^(8)kg`

HOPE THIS HELPS!!