Examkin

Question

Difficulty: HardUnit Conversions

A solar power station consists of solar panels that generate electricity at a constant rate of 15 watts15\text{ watts} per square foot of panel surface area (where 1 watt=1 joule per second1\text{ watt} = 1\text{ joule per second}). The panels have a total surface area of 12,000 square yards12,000\text{ square yards}. How many megajoules (MJ) of energy do the panels generate in 2 hours2\text{ hours}? (Given that 1 yard=3 feet1\text{ yard} = 3\text{ feet} and 1 MJ=1,000,000 joules1\text{ MJ} = 1,000,000\text{ joules})

  1. A
    144144
  2. B
    194.4194.4
  3. C
    3,8883,888
  4. 11,66411,664Answer

Answer

The solar panels generate 11,66411,664 megajoules of energy in 2 hours2\text{ hours}.
To find the energy generated, first convert the area from square yards to square feet. Since 1 yard=3 feet1\text{ yard} = 3\text{ feet}, 1 square yard=(3 feet)2=9 square feet1\text{ square yard} = (3\text{ feet})^2 = 9\text{ square feet}. Multiplying 12,000 square yards12,000\text{ square yards} by 99 gives 108,000 square feet108,000\text{ square feet}. The power generated is 108,000 square feet×15 watts/square foot=1,620,000 watts108,000\text{ square feet} \times 15\text{ watts/square foot} = 1,620,000\text{ watts}, which is 1,620,000 joules per second1,620,000\text{ joules per second}. In 2 hours2\text{ hours}, which is 2×3,600=7,200 seconds2 \times 3,600 = 7,200\text{ seconds}, the total energy generated is 1,620,000 joules/second×7,200 seconds=11,664,000,000 joules1,620,000\text{ joules/second} \times 7,200\text{ seconds} = 11,664,000,000\text{ joules}. Since 1 MJ=1,000,000 joules1\text{ MJ} = 1,000,000\text{ joules}, this is equivalent to 11,664 MJ11,664\text{ MJ}.

Step-by-Step Solution

1
Convert the surface area of the solar panels from square yards to square feet.
Since 1 yard=3 feet1\text{ yard} = 3\text{ feet}, 1 square yard=32=9 square feet1\text{ square yard} = 3^2 = 9\text{ square feet}. Therefore, the total area in square feet is 12,000×9=108,000 square feet12,000 \times 9 = 108,000\text{ square feet}.
To apply the generation rate given in watts per square foot, the area must be in square feet.
2
Determine the total rate of energy generation in joules per second.
The total power generated is 108,000 square feet×15 watts per square foot=1,620,000 watts108,000\text{ square feet} \times 15\text{ watts per square foot} = 1,620,000\text{ watts}. Since 1 watt=1 joule per second1\text{ watt} = 1\text{ joule per second}, this equals 1,620,000 joules per second1,620,000\text{ joules per second}.
This calculates the total energy produced by the entire solar farm every second.
3
Convert the total time from hours to seconds.
2 hours×60 minutes/hour×60 seconds/minute=7,200 seconds2\text{ hours} \times 60\text{ minutes/hour} \times 60\text{ seconds/minute} = 7,200\text{ seconds}.
To find the total energy generated, the rate (joules per second) must be multiplied by the duration in seconds.
4
Calculate the total energy generated in joules, then convert it to megajoules (MJ).
Total energy in joules is 1,620,000 joules/second×7,200 seconds=11,664,000,000 joules1,620,000\text{ joules/second} \times 7,200\text{ seconds} = 11,664,000,000\text{ joules}. Converting to megajoules: 11,664,000,000 joules÷1,000,000 joules/MJ=11,664 MJ11,664,000,000\text{ joules} \div 1,000,000\text{ joules/MJ} = 11,664\text{ MJ}.
This yields the final quantity of energy in the requested units.

Key Concept

Multi-step unit conversions involving area scaling, compound rates, and time conversions.
Estimated Time:2m 30s
Rate this question

Topics

Unit Conversions

More questions from this topic