A nuclear burning power plant produces a total power of 1.1kW. It serves a community that requires 2.85 x 107 kJ of power over the entire year. How many days per year does the power plant need to operate to provide all this power?
300 days
250 days
365 days
200 days
150 days
1.1kW = 1.1kJ/s
T = 2.85*10^7kJ * 1s./1.1kJ * 1h/3600s *
1day/24h = 300 Days.
To determine the number of days per year the power plant needs to operate to provide the required power, we can use the equation:
Energy = Power x Time
First, let's convert the power generated by the nuclear burning power plant into joules. Since 1 kilowatt (kW) is equal to 1000 joules per second (J/s), we can convert 1.1 kW to joules per second:
1.1 kW = 1.1 x 1000 J/s = 1100 J/s
Next, we need to find out how much time is needed to produce 2.85 x 10^7 kJ (kilojoules). Since 1 kJ is equal to 1000 joules (J), we can convert 2.85 x 10^7 kJ to joules:
2.85 x 10^7 kJ = 2.85 x 10^7 x 1000 J = 2.85 x 10^10 J
Now, we can use the equation Energy = Power x Time to find the time:
2.85 x 10^10 J = 1100 J/s x Time
Dividing both sides of the equation by 1100 J/s, we get:
Time = (2.85 x 10^10 J) / (1100 J/s) = 2.59 x 10^7 s
Since we want to find the number of days, we need to convert seconds to days. There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute:
1 day = 24 hours x 60 minutes x 60 seconds = 86400 seconds
Therefore, the number of days the power plant needs to operate can be calculated as:
Time (days) = (2.59 x 10^7 s) / (86400 s/day) ≈ 299.87 days
Rounding to the nearest whole number, the power plant needs to operate for approximately 300 days to provide all the required power. Hence, the correct answer is 300 days.