Normally the rate at which you expend energy
during a brisk walk is 3.6 Calories per minute.
(A Calorie is the common unit of food energy,
equal to 4184.1 J.)
How long do you have to walk to produce
the same amount of energy as a 100 W lightbulb that is lit for 8.4 hours?
Answer in units of h
energy=100 joules/sec*8.4hrs*3600sec/hr
time to walk=energyabove/4184*3.6 minutes
To find out how long you have to walk to produce the same amount of energy as a 100 W light bulb that is lit for 8.4 hours, we need to calculate the total energy expended by the light bulb.
First, we need to convert the power of the light bulb from Watts to energy in Joules. The formula to calculate energy is:
Energy (in Joules) = Power (in Watts) × Time (in seconds)
Since the time given is in hours, we need to convert it to seconds. There are 60 seconds in a minute and 60 minutes in an hour, so:
Time (in seconds) = 8.4 hours × 60 minutes/hour × 60 seconds/minute
Next, we calculate the energy:
Energy (in Joules) = 100 W × (8.4 hours × 60 minutes/hour × 60 seconds/minute)
Now, we can convert the energy expended during a brisk walk from Calories to Joules. We know that 1 Calorie is equal to 4184.1 Joules, so:
Energy (in Joules) = 3.6 Calories/minute × Time (in minutes) × 4184.1 Joules/Calorie
Now, we can equate the two energy values and solve for the time in minutes:
3.6 Calories/minute × Time (in minutes) × 4184.1 Joules/Calorie = Energy (in Joules)
Simplifying the equation:
Time (in minutes) = Energy (in Joules) / (3.6 Calories/minute × 4184.1 Joules/Calorie)
Converting the time from minutes to hours:
Time (in hours) = Time (in minutes) / 60
Substituting the values and solving for time:
Time (in hours) = (100 W × (8.4 hours × 60 minutes/hour × 60 seconds/minute)) / (3.6 Calories/minute × 4184.1 Joules/Calorie)
To find out how long you have to walk to produce the same amount of energy as a 100 W lightbulb that is lit for 8.4 hours, we need to calculate the total energy consumed by the lightbulb and then divide it by the rate at which energy is expended during a brisk walk.
First, let's calculate the energy consumed by the lightbulb. The power of the lightbulb is given as 100 W and it is lit for 8.4 hours. We can use the formula:
Energy = Power * Time
Energy = 100 W * 8.4 hours
However, we need to convert hours to minutes, as the energy expended during a brisk walk is given in Calories per minute. There are 60 minutes in an hour, so 8.4 hours is equal to 8.4 hours * 60 minutes/hour.
Energy = 100 W * (8.4 hours * 60 minutes/hour)
Now, let's convert the energy from Joules to Calories. We know that 1 Calorie is equal to 4184.1 J, so we can divide the energy obtained in Joules by this conversion factor to get the energy in Calories.
Energy (in Calories) = Energy (in J) / 4184.1 J/Calorie
Now, let's substitute the energy obtained from the previous calculation into this formula to calculate the energy consumed by the lightbulb in Calories.
Energy (in Calories) = (100 W * (8.4 hours * 60 minutes/hour)) / 4184.1 J/Calorie
Finally, to find out how long you have to walk to produce the same amount of energy, we divide the energy consumed by the lightbulb in Calories by the rate at which energy is expended during a brisk walk, which is 3.6 Calories per minute.
Time = Energy (in Calories) / Energy expended during a brisk walk
Time = (100 W * (8.4 hours * 60 minutes/hour)) / (3.6 Calories/minute)
Now, let's calculate the result:
Time = (100 * 8.4 * 60) / 3.6
Time = 10080 / 3.6
Time = 2800
Therefore, you would have to walk for 2800 minutes to produce the same amount of energy as a 100 W lightbulb that is lit for 8.4 hours. To convert this to hours, divide the value by 60 (since there are 60 minutes in an hour):
Time (in hours) = 2800 minutes / 60 minutes/hour
Time (in hours) = 46.67 hours
Hence, you would have to walk for approximately 46.67 hours to produce the same amount of energy as a 100 W lightbulb that is lit for 8.4 hours.