Questions: Use the following energy conversion factors to complete the table below: 1 calorie (cal) = 4.184 joules (J) 1 Calorie (Cal) = 1000 calories (cal) 1 kilowatt-hour (kWh) = 3.60 x 10^6 joules (J) J cal Cal kWh ------------ 5.38 x 10^-2 J 1.29 x 10^-2 cal 125 kWh

Use the following energy conversion factors to complete the table below: 1 calorie (cal) = 4.184 joules (J) 1 Calorie (Cal) = 1000 calories (cal) 1 kilowatt-hour (kWh) = 3.60 x 10^6 joules (J) J cal Cal kWh ------------ 5.38 x 10^-2 J 1.29 x 10^-2 cal 125 kWh
Transcript text: Use the following energy conversion factors to complete the table below: 1 calorie (cal) $=4.184$ joules (J) 1 Calorie $(\mathrm{Cal})=1000$ calories (cal) 1 kilowatt-hour (kWh) $=3.60 \times 10^{6}$ joules (J) \begin{tabular}{|c|c|c|c|} \hline J & cal & Cal & kWh \\ \hline $5.38 \times 10^{-2} \mathrm{~J}$ & $1.29 \times 10^{-2} \mathrm{cal}$ & & \\ \hline & & & 125 kWk \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Convert Joules to Calories

To convert joules to calories, use the conversion factor \(1 \, \text{cal} = 4.184 \, \text{J}\).

Given: \(5.38 \times 10^{-2} \, \text{J}\)

\[ \text{cal} = \frac{5.38 \times 10^{-2} \, \text{J}}{4.184 \, \text{J/cal}} = 1.286 \times 10^{-2} \, \text{cal} \]

This value is approximately \(1.29 \times 10^{-2} \, \text{cal}\), which matches the given value in the table.

Step 2: Convert Kilowatt-hours to Joules

To convert kilowatt-hours to joules, use the conversion factor \(1 \, \text{kWh} = 3.60 \times 10^{6} \, \text{J}\).

Given: \(125 \, \text{kWh}\)

\[ \text{J} = 125 \, \text{kWh} \times 3.60 \times 10^{6} \, \text{J/kWh} = 4.50 \times 10^{8} \, \text{J} \]

Step 3: Convert Joules to Calories and Calories

First, convert joules to calories using the conversion factor \(1 \, \text{cal} = 4.184 \, \text{J}\).

\[ \text{cal} = \frac{4.50 \times 10^{8} \, \text{J}}{4.184 \, \text{J/cal}} = 1.075 \times 10^{8} \, \text{cal} \]

Next, convert calories to Calories using the conversion factor \(1 \, \text{Cal} = 1000 \, \text{cal}\).

\[ \text{Cal} = \frac{1.075 \times 10^{8} \, \text{cal}}{1000 \, \text{cal/Cal}} = 1.075 \times 10^{5} \, \text{Cal} \]

Final Answer

\[ \begin{array}{|c|c|c|c|} \hline \text{J} & \text{cal} & \text{Cal} & \text{kWh} \\ \hline 5.38 \times 10^{-2} & 1.29 \times 10^{-2} & & \\ \hline 4.50 \times 10^{8} & 1.075 \times 10^{8} & 1.075 \times 10^{5} & 125 \\ \hline \end{array} \]

\[ \boxed{ \begin{array}{|c|c|c|c|} \hline \text{J} & \text{cal} & \text{Cal} & \text{kWh} \\ \hline 5.38 \times 10^{-2} & 1.29 \times 10^{-2} & & \\ \hline 4.50 \times 10^{8} & 1.075 \times 10^{8} & 1.075 \times 10^{5} & 125 \\ \hline \end{array} } \]

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