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

Solution Steps

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.

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

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

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

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