Question

Even when shut down after a period of normal use, a large commercial nuclear reactor produces heat at the rate of 142 MW by the radioactive decay of fission products. This causes a rapid increase in temperature if the cooling system fails (a) Calculate the rate of temperature increase in degrees Celsius per second (°C/S), if the mass of the reactor core is 1.60 x 10° kg and has an average specific heat of 0.0800 kcal/(kg·°C) oC/s (b) How long would it take to obtain a temperature increase of 1600°C? (The initial rate of temperature increase would be greater than calculated here, because the heat is concentrated in a smaller mass, but later, the temperature increase would slow because the 5 × 105 kg steel containment vessel would begin to be heated, too.

Answer 1

Solution,

A)

Q = m c dT

Here, Q = heat, m = mass, c = specific heat and dT = change in temperature

Since, Q = Power x time

So, power, P = Q/dt

P = m c dT/dt

142 x 10^6 = 1.6 x 10^5 x 0.08 x 4186 x dT/dt

dT/dt = 2.65 degree C/s

B)

delta T = t (dT/dt)

1600 = t x 2.65

t = 603.73 sec

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