Even when shut down after a period of normal use, a large commercial nuclear rea

Question

Even when shut down after a period of normal use, a large commercial nuclear reactor transfers thermal energy at the rate of 110 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 1 W = 1 J/s and W = 1 megawatt).

(a) Calculate the rate of temperature increase in degrees Celsius per second (°C/s), if the mass of the reactor core is 1.60 105 kg and has an average specific heat of 0.0800 kcal/kg · °C.

____°C/s

(b) How long would it take to obtain a temperature increase of 2200°C, which could cause some metals holding the radioactive materials to melt? (The initial rate of temperature increase would be greater than calculated here because the heat is concentrated in a smaller mass. Later, however, the temperature increase would slow because the 5 105 kg steel containment vessel would also begin to be heat up.)

____ s

Explanation / Answer

a )

given P = 110 MW = 110 X 106 W

using equation P = Q / t

P = m C dT / t

110 X 106 = 1.6 X 105 X 0.08 X 4186 X dT / t

dT / t = 110 X 106 / 1.6 X 105 X 0.08 X 4186

dT / t = 2.05oC/sec

b )

dT / t = 2.05oC/sec

2200 / t = 2.05

t = 2200 / 2.05

t = 1073.17 sec

or

t = 1073.17 / 60 = 17.88 min

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