In a serious accident,a neclear plant's reactor vessal cracks,and all of the cooling water drains out.Although nuclear fission stops,readioactive decay continues to heat the reactor's 2.5 x 10^5 kg uranium core at a rate of 120 Mega-Watts.Once the core reaches its melting point,how much energy will it takes to melt the core? How long will the melting take?
massuranium*Heatfusion=energy
How long? energy/120MegaWatts=timeinseconds
To determine the energy required to melt the uranium core, we first need to calculate the total energy needed to raise the core's temperature to its melting point, and then add the energy required for the phase change from solid to liquid.
1. Calculating the energy required to raise the temperature:
The specific heat capacity of uranium is approximately 115 J/kg·K. The melting point of uranium is around 1405°C or 1678 K (Kelvin). To raise the temperature of the core from room temperature (let's assume 25°C or 298 K) to its melting point, we can use the formula:
Energy = mass × specific heat capacity × change in temperature
Given:
Mass of uranium core (m) = 2.5 x 10^5 kg
Specific heat capacity of uranium (c) = 115 J/kg·K
Change in temperature (ΔT) = Melting point temperature - Room temperature
= 1678 K - 298 K
Energy = (2.5 x 10^5 kg) × (115 J/kg·K) × (1678 K - 298 K)
2. Calculating the energy required for phase change:
The heat of fusion (energy required for the solid to liquid phase change) for uranium is approximately 235,000 J/kg.
Energy = mass × heat of fusion
Given:
Mass of uranium core (m) = 2.5 x 10^5 kg
Heat of fusion of uranium (Lf) = 235,000 J/kg
Energy = (2.5 x 10^5 kg) × (235,000 J/kg)
To find the total energy required to melt the uranium core, add the energy calculated in step 1 and step 2.
Total Energy = Energy (temperature rise) + Energy (phase change)
Finally, to determine the time it takes to melt the core, we need to calculate the rate at which energy is being supplied (decay heat) and divide the total energy required by this rate.
Decay heat = 120 Mega-Watts = 120 x 10^6 Watts
Time = Total Energy / Decay heat
Please note that these calculations provide an approximation and actual scenario may differ.