Incorrect Calculation of Time for Reactor Energy Phase Change

AI Thread Summary
The calculation for the time required for the reactor's energy phase change was initially set up incorrectly. The equation Q'*t = Q1 + Q2 was used, where Q' is the reactor's energy of 200,000 kJ, and Q1 and Q2 were based on half the mass of water for boiling and the total mass for heating to 100 degrees Celsius, respectively. The correct approach requires using half the mass for Q1, as only half the water is being boiled off, while Q2 should use the total mass to account for heating all the water to boiling point. This adjustment led to a more accurate calculation of the time needed for the phase change. Properly applying the mass values is crucial for accurate energy calculations in phase changes.
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Homework Statement
If 4.5×10^5kg of emergency cooling water at 10 ∘C are dumped into a malfunctioning nuclear reactor whose core is producing energy at the rate of 200 MW , and if no circulation or cooling of the water is provided, how long will it be before half the water has boiled away?
Relevant Equations
Q1=Lm
Q2=mc T
m=4.5*10^5
L=2257 kj/kg
c=4.184 kj/kg*K
I tried using the equation Q'*t= Q1+Q2. Where Q' is the energy of the reactor aka 200,000 kJ and t is the time. Take Q1 to be (1/2m*2257) and Q2 to be (1/2m*4.184*90). The 90 is the change in temperature for the phase change to occur from liquid water to gas, or boiling. Plugged everything in and got 2962.755 seconds. Convert to minutes by dividing by 60 seconds to get 49.379 minutes. This answer was wrong. Can anyone tell me what is wrong with this setup?
 
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I figured it out. What needs to happen the mass for Q1 needs to be the total mass divided by 2. The Q2 mass needs to be the total mass. This is because 1/2 of the water is being boiled off, but the total amount of water needs to reach the 100 degrees Celsius.
 
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