78. A nuclear power plant generates 1000 Megawatts (MW) of electrical power and used half of its fuel supply in 5 years. The reactor uses 235U with 33% efficiency for the conversion of heat released by nuclear fission to electrical power. Each atom of 235U releases 200 MeV of energy. How many tons of 235U did the reactor start with? (1 ton = 1000 kg; Avogadro number = 6.023 × 1023 mol–1)
Midnight Sun Area Ratio When the Earth’s Axial Tilt Changes
Concept Used
The regions experiencing the Midnight Sun lie beyond the polar circles. If the Earth’s axis makes an angle α with the plane of the ecliptic, then the latitude of the polar circle is also α.
The area of one polar cap extending from latitude L to the pole is
A = 2πR²(1 − sin L)
Since both polar regions are considered over a full year, the factor of 2 cancels when taking the ratio.
Step 1: Previous Midnight Sun Area
Initially,
L₁ = 66.5°
Therefore,
A₁ ∝ (1 − sin66.5°)
Step 2: New Midnight Sun Area
After the axis changes,
L₂ = 50°
Therefore,
A₂ ∝ (1 − sin50°)
Step 3: Calculate the Ratio
The required ratio is
A₂/A₁ = (1 − sin50°)/(1 − sin66.5°)
Using
- sin50° ≈ 0.7660
- sin66.5° ≈ 0.9171
Hence,
A₂/A₁ = (1 − 0.7660)/(1 − 0.9171)
= 0.2340/0.0829
≈ 2.82
Physical Interpretation
Reducing the angle from 66.5° to 50° moves the polar circles much closer to the equator. As a result, a much larger portion of the Earth’s surface experiences 24-hour daylight during summer. Therefore, the Midnight Sun region increases significantly.
Final Answer
The ratio of the new area to the previous area is
2.82 (approximately)
