Question

A typical nuclear reactor generates 1000MW (1000MJ/s of electrical energy. In doing so, it produces 2000MW 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 18C. State regulations limit the temperature of the output water to 30C so as not to harm aquatic organisms. How many liters of cooling water have to be pumped through the reactor each minute?

Answer 1

Answer:

2391200 L/min

Explanation:

$\dot{E} = 2000MW = 2000MJ/s = 2\times10^9J/s$

Let water capacity $c_w$ = 4182 Jkg/C and water density ρ be 1 kg/L

For each second we need to dissipate $2\times10^9J$ of heat on 18C water to 30C water. We can use the following heat exchange equation to find out the mass rate

$\dot{E} = \dot{m}c_w\Delta T$

$2\times10^9 = \dot{m}4182(30-18)$

$\dot{m} = \frac{2\times10^9}{4182*12} = 39853 kg/s$

$\dot{V} = \dot{m}/\rho = 39853/1 = 39853 Liters/s = 39853 * 60 = 2391200 L/min$