A 20 fluid oz. soda contains 238 Calories. (a) How many kilojoules does the soda contain? (b) For how many hours could the amount of energy in the soda light a 75-watt light bulb? (1 watt = 1 J/s)

Verified step by step guidance

Step 1: Convert Calories to kilocalories. Since 1 Calorie (with an uppercase 'C') is equivalent to 1 kilocalorie (kcal), the soda contains 238 kcal.

Step 2: Convert kilocalories to kilojoules. Use the conversion factor: 1 kcal = 4.184 kJ. Multiply 238 kcal by 4.184 kJ/kcal to find the energy in kilojoules.

Step 3: Calculate the total energy in joules. Since 1 kJ = 1000 J, multiply the energy in kilojoules by 1000 to convert it to joules.

Step 4: Determine the energy consumption of a 75-watt light bulb. Since 1 watt = 1 J/s, a 75-watt bulb uses 75 J every second.

Step 5: Calculate the number of hours the light bulb can be powered. Divide the total energy in joules by the energy consumption rate of the bulb (75 J/s) to find the time in seconds, then convert seconds to hours by dividing by 3600 (the number of seconds in an hour).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Energy Conversion

Energy can be expressed in different units, such as calories and joules. To convert calories to joules, the conversion factor is 1 calorie = 4.184 joules. In this question, understanding how to convert the energy content of the soda from calories to kilojoules (1 kilojoule = 1000 joules) is essential for solving part (a).

Power and Energy Relationship

Power is defined as the rate at which energy is used or transferred, measured in watts (W), where 1 watt equals 1 joule per second (J/s). To determine how long the energy from the soda can power a light bulb, one must relate the total energy available (in joules) to the power consumption of the bulb. This relationship is crucial for solving part (b) of the question.

Unit Consistency

When performing calculations involving different units, it is vital to ensure that all units are consistent. In this problem, energy must be expressed in joules to match the power of the light bulb in watts. Maintaining unit consistency throughout the calculations will prevent errors and ensure accurate results.

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