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 produces heat at the rate of 140 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 1.60 105 kg and has an average specific heat of 0.0800 kcal/kg·°C. 2.8 Incorrect: Your answer is incorrect. °C/s (b) How long would it take to obtain a temperature increase of 2200°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.) s

Explanation / Answer

here ,

rate of production of energy ,

P = 140 *10^6 W

a) let the rate of increase of temperature is dT/dt

as P = m * S * dT/dt

140 *10^6 = 1.6 *10^5 * 0.080 * 4186 * dT/dt

dT/dt = 2.62 degree C/s

the rate of temperature increase is 2.62 degree C/s

b)

let the time taken is t

t * dT/dt = delta T

t * 2.62 = 2200

t = 842 s

the time taken for the temperature increase of 2200 degree C is 842 s

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