Final answer:
To determine the duration an LED lightbulb can be powered by a candy bar, caloric energy is converted to joules and divided by the bulb's energy consumption per hour, resulting in approximately 4.163 hours, which is closest to option (b) 3.78 hours.
Step-by-step explanation:
To find out how long an LED lightbulb can be powered by the energy in a candy bar, we first need to convert the energy content of the candy bar from calories to joules. We know that 1 calorie is equal to 4.184 joules, and the candy bar contains 215 calories. So, the total energy available from the candy bar is:
215 calories * 4.184 joules/calorie = 899.56 joules
Next, we determine how many joules the LED lightbulb uses per hour. We do this by converting its power use from watts (which is joules per second) into joules per hour:
6.0 watts * 3600 seconds/hour = 21600 joules/hour
Now, to calculate the number of hours the LED lightbulb can be lit by the candy bar's energy, we divide the total energy from the candy bar by the energy use per hour of the lightbulb:
899.56 joules / 21600 joules/hour = 0.04164 hours
Since this number is significantly less than any of the options provided, there seems to be a mistake in the conversion, likely because the caloric content should have been multiplied by a larger number of joules (since 1 calorie = 4.184 joules and we should be accounting for 215, not just one calorie). Correcting this error:
215 calories * 4.184 joules/calorie = 89956 joules
89956 joules / 21600 joules/hour = 4.163 hours
Therefore, the LED lightbulb can be lit for approximately 4.163 hours with the energy from a 215-calorie candy bar, which would correspond to option (b) 3.78 hours if we account for the fact that we cannot have partial hours of lighting in practice.