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Chapter 4: Problem 478

An ice-cream has a marked value of \(700 \mathrm{kcal}\). How many kilo-watt- hour of energy will it deliver to the body as it is digested $(\mathrm{J}=4.2 \mathrm{~J} / \mathrm{cal})$ (A) \(0.81 \mathrm{kwh}\) (B) \(0.90 \mathrm{kwh}\) (C) \(1.11 \mathrm{kwh}\) (D) \(0.71 \mathrm{kwh}\)

Short Answer

Expert verified
The ice-cream delivers 0.82 kWh to the body when digested, and the closest option is (A) 0.81 kWh.

Step by step solution

01

Convert kilocalories to calories

To convert the energy in kilocalories to calories, multiply the given value by 1000: Energy = 700 kcal × 1000 cal/kcal = 700,000 cal
02

Convert calories to Joules

Next, we need to convert this energy from calories to Joules using the provided conversion factor 1 cal = 4.2 J: Energy = 700,000 cal × 4.2 J/cal = 2,940,000 J
03

Convert Joules to kilowatt-hours

Finally, we need to convert the energy from Joules to kilowatt-hours. We know that 1 kWh = 3,600,000 J. Therefore, Energy = \( \frac{2,940,000 \mathrm{J}}{3,600,000 \mathrm{J/kWh}} = 0.8167 \mathrm{kWh} \)
04

Round the answer and choose the correct option

Round the result to two decimal places: Energy = 0.82 kWh Comparing our result to the available options, the closest value is (A) 0.81 kWh.

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