Question 9.F.1: During the nuclear reactor accident at Three Mile Island in ......

During the nuclear reactor accident at Three Mile Island in 1979, an unknown mass of fuel pellets melted, allowing some of the fuel material to fall into water at the bottom of the reactor. Assume that the melting fuel pellets were pure UO_2 and had resolidified and cooled to 900°C before reaching the water. Further assume that the water was initially at 8°C and that sensors indicated the final temperature of the water was 85°C.

(a) What information would you have to look up to determine the mass of fuel pellets that fell into the water?

(b) What would you have to know to use this information to determine the percentage of the fuel that melted in the accident? How would you calculate the percentage?

Strategy

(a) The first question that must be addressed is, “What sources of heat raised the temperature of the water?” Were the fuel pellets the only thing that melted? Because we have no other information, we will assume that the only important heat flow was between the pellets and the water. If that were not true, then we would need to account for other materials in our handling of this problem. If the assumption turns out to be incorrect, we will overestimate the amount of fuel that melted in the accident.

Once we have made the assumption that the melted fuel is the only source of heat for the water, we would set up a heat balance between the water and the fuel pellets. Thus

q_{\text{pellets}} = –q_{\text{water}}

and

(m c\Delta T)_{\mathrm{pellets}}=-(mc\Delta T)_{\mathrm{water}}

We can see there are six possible variables in this equation. Which do we know and which can be looked up? Both ΔT values are known. The initial temperatures of both the water and the fuel pellets were given in the problem and both share the final temperature of 85°C. The specific heat (c) is not given for either the water or the fuel pellets. This is information that must be looked up, but it should be available from standard reference sources.

That leaves the two masses, and clearly the goal of the exercise is to find the mass of the melted fuel pellets. But we don’t know the mass of the water involved, either. So either we must find some way to look up this value or we must make a reasonable estimate.

(b) This part of the question assumes that we can find the mass from part (a). If that’s true, then we would need to know the total mass of fuel pellets initially present. This number must be looked up or estimated based on some reliable information.