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

Answer:

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

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

Answer:

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

Explanation:

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

$E=\Delta mc^2\\\Delta m=\frac{E}{c^2}$(1)

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

$E=Pt=2.3*10^{9}\frac{J}{s}*1 year*\frac{365.25 day}{1 year}*\frac{24h}{1 day}*\frac{3600s}{1h}=7.25*10^{16}J$

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

$\Delta m=\frac{7.25*10^{16}J}{3*10^{8}\frac{m}{s}}=2.41*10^{8}kg$

HOPE THIS HELPS!!