Final answer:
When calculating the energy transfer rate at a refueling station with the given data (6 gallons per minute and gasoline's energy content of 34 MJ per liter), the result is approximately 13 MW, which is similar to the 15 MW claim.
Step-by-step explanation:
To verify the claim that a car refueling at a gasoline station is transferring energy at a rate of approximately 15 MW, we must calculate the energy transfer rate using the given data: the refueling rate of 6 gallons (or 23 liters) per minute and the energy content of gasoline, which is about 34 MJ per liter.
First, we find the total energy transferred per minute by multiplying the volume by the energy content per liter:
Energy per minute = Volume per minute × Energy content per liter
Energy per minute = 23 L/min × 34 MJ/L
This gives us an energy transfer rate of 782 MJ/min (since 23 × 34 = 782). To convert this to watts, we note that 1 watt is equal to 1 joule per second. Hence, 782 MJ/min is equivalent to (782 × 106) joules/60 seconds, because there are 60 seconds in a minute.
Energy transfer rate = (782 × 106 J/min) ÷ (60 s/min)
Energy transfer rate = 13,033,333 W, or approximately 13 MW.
While the calculated energy transfer rate is approximately 13 MW, which is slightly less than the stated rate of 15 MW in the claim, it's indeed in the same neighborhood. The discrepancy can be due to rounding or differences in the specific energy content of gasoline.