Final answer:
To find the ratio of the mass of coal to uranium-235, calculate the total energy output of a power plant per day, and divide this by the energy released per kg of coal and per fission of uranium-235. Afterwards, the masses of coal and uranium-235 needed are computed and the required ratio is determined.
Step-by-step explanation:
The question asks us to compare the mass of coal burned to the mass of uranium-235 that undergoes fission in two power plants with the same efficiency operating a 1000-MW power output for one day. To calculate this ratio, we first need to determine the total energy produced by the 1000-MW plant in one day, which can be found using the formula: Energy (in joules) = Power (in watts) x Time (in seconds). Since there are 86,400 seconds in a day (24 hours x 60 minutes x 60 seconds), and considering the 40% efficiency of the plants, the total energy required from the fuel source can be calculated.
Using the given information that the energy released by burning coal is 3.3×10· J/kg and the energy released per uranium-235 fission is 200 MeV (which can be converted to 3.2×10±³ J/fission), we then find how much coal and uranium-235 are required to produce the necessary energy. To do this, we divide the total energy by the energy per kg of coal and by the energy per fission of uranium-235, respectively, taking into account Avogadro's number to find the mass of uranium-235. Finally, we find the ratio of coal mass to uranium-235 mass required.