Question

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 if the cooling system fails (1 watt = 1 joule/second or (1W=1J/s) and (1MW=1 megawatt)). (a) Calculate the rate of temperature increase in degrees Celsius per second (°C/s) if the mass of the reactor core is (1.60×10^5 kg) and it has an average specific heat of (0.3349 kJ/kg·°C). (b) How long would it take to obtain a temperature increase of (2000°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 (500,000-kg) steel containment vessel would also begin to heat up.)

a) Calculate the rate of temperature increase and discuss its significance.
b) Determine the time required for a (2000°C) temperature increase.

Answer 1

The rate of temperature increase in the reactor is approximately 0.223°C/s. It would take approximately 8989 seconds (2.5 hours) to obtain a temperature increase of 2000°C.

Step-by-step explanation:

To calculate the rate of temperature increase in degrees Celsius per second (°C/s), we need to use the formula:

Rate of temperature increase = (Rate of heat transfer) / (Mass x Specific heat)

Using the given values, the rate of heat transfer is 150 MW (which can be converted to 150 x 10^6 W) and the mass of the reactor core is 1.60 x 10^5 kg. The specific heat is 0.3349 kJ/kg · °C (which can be converted to 334.9 J/kg · °C).

Substituting these values into the formula, we get:

Rate of temperature increase = (150 x 10^6 W) / (1.60 x 10^5 kg x 334.9 J/kg · °C)

Simplifying the equation, we find that the rate of temperature increase is approximately 2.23 x 10^-1°C/s.

To determine the time required for a temperature increase of 2000°C, we can use the formula:

Time = (Change in temperature) / (Rate of temperature increase)

Substituting the values, we get:

Time = 2000°C / 2.23 x 10^-1°C/s

Calculating this, we find that the time required to obtain a temperature increase of 2000°C would be approximately 8989 seconds or 2.5 hours.