Chapter 14, Problem 10PE

Even when shut down after a period of normal use, a large commercial nuclear reactor transfers thermal energy at the rate of 150 MW by the radioactive decay of fission products. This heat transfer causes a rapid increase in temperature it the cooling system fails (1 watt 2 1 joule/second or $\text{1 W}=\text{1 J}/\text{s}$ and $\text{1 MW}=\text{1 megawatt}$ ). (a) Calculate the rate of temperature increase in degrees Celsius per second $\left(°\text{C}/\text{s}\right)$ if the mass of the reactor core is $1.60\times {10}^5\text{kg}$ and it has an average specific heat of $0.3349\text{kJ/kg}°\cdot \text{C}$. (b) How long would it take to obtain a temperature increase of $\text{2}000°\text{C}$, which could cause some metals holding the radioactive materials to melt? (The initial rate of temperature increase would be greater than that calculated here because the heat transfer is concentrated in a smaller mass. Later, however, the temperature increase would slow down because the $5\times {10}^5\text{-kg}$ steel containment vessel would also begin to heat up.)

Figure 14.32 Radioactive spent−fuel pool at a nuclear power plant.

Spent fuel stays hot for a long time. (credit: U.S. Department of Energy)