Incorrect Calculation of Time for Reactor Energy Phase Change

In summary, the conversation is about using an equation to calculate the time it takes for a phase change to occur in a reactor. The equation used is Q'*t = Q1 + Q2, with Q' being the energy of the reactor, t being the time, Q1 being half the mass of water multiplied by 2257, and Q2 being half the mass of water multiplied by 4.184 and 90 representing the change in temperature from liquid water to gas. After plugging in all the values, the calculation yielded 49.379 minutes, which was later found to be incorrect. The mistake was identified as not considering the total mass of water in Q1 and Q2 calculations. Q1 should be the total
  • #1
runningphysics
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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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  • #2
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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1. What is the importance of accurately calculating the time for reactor energy phase change?

The accurate calculation of time for reactor energy phase change is crucial for the safe and efficient operation of a nuclear reactor. It ensures that the reactor is not operating at a critical state for too long, which can lead to overheating and potential meltdowns. Additionally, accurate time calculations help with the scheduling of maintenance and refueling, which are essential for the longevity of the reactor.

2. What factors can lead to an incorrect calculation of time for reactor energy phase change?

There are several factors that can contribute to an incorrect calculation of time for reactor energy phase change. These include human error, equipment malfunctions, and external factors such as power outages or natural disasters. It is essential to regularly review and update the calculations to account for any changes in these factors.

3. How can incorrect time calculations impact the reactor?

Incorrect time calculations can have severe consequences for the reactor and its surrounding environment. If the reactor is operating at a critical state for too long, it can lead to overheating, which can result in a nuclear meltdown. This can release harmful radiation into the environment and pose a threat to public health and safety.

4. How can scientists ensure accurate time calculations for reactor energy phase change?

To ensure accurate time calculations, scientists must use reliable and up-to-date data, perform regular checks and reviews, and use advanced computer simulations. It is also essential to have a team of experienced and knowledgeable scientists and engineers overseeing the calculations and making any necessary adjustments.

5. What measures can be taken to prevent incorrect time calculations for reactor energy phase change?

To prevent incorrect time calculations, it is crucial to have strict quality control measures in place. This includes regular reviews and updates of the calculations, using multiple methods to cross-check the results, and implementing safety protocols in case of any miscalculations. It is also essential to invest in advanced technology and training for the scientists and engineers responsible for the calculations.

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