Question

If a gas stove releases \(120 \mathrm{~kJ}\) of heat energy, what is the energy in kilocalories? \((1 \mathrm{cal}=4.184 \mathrm{~J})\).

Short answer

28.68 kcal.

Step-by-step solution

Convert Kilojoules to Joules

First, convert the heat energy from kilojoules (kJ) to joules (J). Since 1 kJ equals 1000 J, we have: \[ 120 \text{ kJ} = 120 \times 1000 \text{ J} = 120000 \text{ J} \]

Convert Joules to Calories

Next, convert the energy from joules to calories, using the conversion factor: 1 calorie (cal) = 4.184 joules (J). Thus, \[ \text{Calories} = \frac{120000 \text{ J}}{4.184 \text{ J/cal}} \approx 28677.85 \text{ cal} \]

Convert Calories to Kilocalories

Finally, convert calories to kilocalories. Since there are 1000 calories in a kilocalorie, divide the number of calories by 1000: \[ \text{Kilocalories} = \frac{28677.85 \text{ cal}}{1000} \approx 28.68 \text{ kcal} \]

Key concepts

Kilojoules to Joules

When converting energy measurements, it's important to know the relationship between kilojoules (kJ) and joules (J). Kilojoules and joules are both units of energy, with joules being the smaller unit. Specifically, 1 kilojoule is equal to 1000 joules.

This conversion is straightforward because it essentially requires multiplying the number of kilojoules by 1000. For instance, if you have 120 kJ of energy, converting it to joules involves a simple calculation:

• Multiply 120 by 1000
• You get 120,000 joules

This conversion is useful in many scientific and engineering contexts where joules are often the standard unit to measure energy more precisely.

Joules to Calories

Understanding how joules relate to calories involves knowing the conversion factor between these units. Calories, often used in nutrition, can be derived from joules using the formula: 1 calorie (cal) = 4.184 joules (J). This factor originates from the definition that 1 calorie is the amount of energy needed to raise the temperature of 1 gram of water by 1 degree Celsius.

To convert joules to calories:

• Take the total joules, and divide by 4.184
• For example, converting 120,000 joules involves: \[\text{Calories} = \frac{120,000 \text{ J}}{4.184 \text{ J/cal}} \approx 28,677.85 \text{ cal}\]

This conversion is essential when discussing energy content in foods, where energy is often reported in calories.

Calories to Kilocalories

Kilocalories, often just called "calories" in everyday language, are used widely in food labels and discussions about energy intake. One kilocalorie (kcal) is equivalent to 1000 calories (cal). This relationship arises from the large amounts of energy involved in metabolic processes.

To convert from calories to kilocalories:

• Divide the number of calories by 1000
• For example, converting 28,677.85 calories results in: \[\text{Kilocalories} = \frac{28,677.85 \text{ cal}}{1000} \approx 28.68 \text{ kcal}\]

This step is crucial for understanding how much energy your body can gain from food, as nutritional energy is commonly expressed in kilocalories.