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 18°C. State regulations limit the temperature of the output water to 30°C so as not to harm aquatic organisms. How many liters of cooling water have to be pumped through the reactor each minute?

Short answer

There are $2.4\times {10}^{6}litre$water release per minutes from pump

Step-by-step solution

Step 1:Definition of specific heat 

The amount of heat that increase1 the degree of the temperature of a 1-mole substance is called specific heat.

Finding the amount of  heat

The cooling power is $P_c=2000MW$

The amount of heat is role="math" localid="1649153822454" $\mathrm{Q}=\mathrm{cm}∆T$

Now new variable of mass M is $\frac{m}{t}$

So, role="math" localid="1649153981842" $$\begin{gathered} \frac{\mathrm{Q}}{\mathrm{t}}=\frac{\mathrm{cm}∆T}{t} \\ {P}_c=cM∆T \\ M=\frac{P_c}{c∆T} \end{gathered}$$

role="math" localid="1649153973102" $$\begin{gathered} M=\frac{m}{t}=\frac{\rho V}{t} \\ V=\frac{Mt}{\rho } \end{gathered}$$

$V=\frac{t{P}_c}{\rho c∆T}$

Applying all values

role="math" localid="1649154122274" $V=\frac{6\times 2\times {10}^9}{1000\times 4180\times 12}=2381M^3/min=2.4\times {10}^{6}litre$