Chapter 17: Problem 6

Verify-showing work-the claim on page 292 that a car refueling at a gasoline station is transferring energy at a rate in the neighborhood of \(15 \mathrm{MW}\) if the transfer rate is about 6 gallons ( \(23 \mathrm{~L}\) ) per minute \(^{32}\) and gasoline contains about 34 MJ per liter.

Short Answer

Expert verified

Question: Verify if the claim that energy transfer during refueling a gasoline takes place at a rate of 15 MW is reasonable, given that gasoline is transferred at a rate of 23 L/min and has an energy content of 34 MJ per liter. Answer: Based on our calculations, the rate of energy transfer during refueling is 13.03 MW, which is close to the given claim of 15 MW. Therefore, it is reasonable to say that the claim is valid.

Step by step solution

Calculate the energy transferred per minute

(First, calculate the amount of energy transferred in one minute by multiplying the quantity of gasoline transferred in liters with the energy content per liter) Quantity of gasoline transferred per minute: 23 L Energy content of gasoline: 34 MJ per liter Energy transferred per minute = (23 L) * (34 MJ per liter)

Calculate the rate of energy transfer in watts

(Next, we need to convert the energy transfer per minute to watts, which are joules per second. To do this, multiply the energy transferred per minute by 1,000,000 to convert megajoules to joules, then divide by 60 to convert minutes to seconds.) Energy transferred per minute = (23 * 34) MJ/min = 782 MJ/min Energy transferred in joules = (782 MJ/min) * (1,000,000 J/MJ) = 782,000,000 J/min Rate of energy transfer = (782,000,000 J/min) / (60 s/min) = 13,033,333.33 W

Convert the rate of energy transfer to megawatts

(Finally, convert the rate of energy transfer from watts to megawatts by dividing by 1,000,000.) Rate of energy transfer = 13,033,333.33 W Rate of energy transfer in megawatts = 13,033,333.33 W / 1,000,000 = 13.03 MW

Compare the calculated value with the given value

(Now, compare the calculated rate of energy transfer in megawatts with the claim on page 292 that the rate of energy transfer is around 15 MW.) Our calculated value is 13.03 MW, which is in the neighborhood of the given claim of 15 MW. Thus, we can verify that the claim on page 292 is reasonable.

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Verify-showing work-the claim on page 292 that a car refueling at a gasoline station is transferring energy at a rate in the neighborhood of \(15 \mathrm{MW}\) if the transfer rate is about 6 gallons ( \(23 \mathrm{~L}\) ) per minute \(^{32}\) and gasoline contains about 34 MJ per liter.

Short Answer

Step by step solution

Calculate the energy transferred per minute

Calculate the rate of energy transfer in watts

Convert the rate of energy transfer to megawatts

Compare the calculated value with the given value

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