A typical nuclear reactor generates 1000 MW ( 1000 MJ/s ) of electrical energy. In doing so, it produces 2000 MW of "waste heat" that must be removed from the reactor to keep it from melting down. Man

Question

A typical nuclear reactor generates 1000 MW ( 1000 MJ/s ) of electrical energy. In doing so, it produces 2000 MW of "waste heat" that must be removed from the reactor to keep it from melting down. Many reactors are sited next to large bodies of water so that they can use the water for cooling. Consider a reactor where the intake water is at 1 8 ∘ C . State regulations limit the temperature of the output water to 3 0 ∘ C so as to not harm aquatic organisms. How many liters (approx) of cooling water have to be pumped through the reactor each minute? Take specific heat of water = 4200 J/kg .

TestHub · Accepted Answer

Waste heat removed per second equals heat taken by the water:
$2000 \times 1 0^{6} = \frac{d m}{d t} \times S \times Δ T$
$2000 \times 1 0^{6} = \frac{d m}{d t} \times 4200 \times 12$
$\frac{d m}{d t} = \frac{20 \times 1 0 ^{6}}{42 \times 12} kg/s$
Per minute:
$\frac{d m}{d t} = \frac{20 \times 1 0 ^{6}}{42 \times 12} \times 60 = \frac{1 0 ^{8}}{42} kg/min$
Since $1 kg$ of water is $1 litre$ :
$\approx 2 \times 1 0^{6} ℓ / min$

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