When 1.0 g of gasoline burns, it releases 11 kcal of heat. The density of gasoline is 0.74 g/mL
a) How many megajoules are released when 3.0 of gasoline burns?
b) If a television requires 150 kJ/h to run, how many hours can the television run on the energy provided by 3.0 gal of gasoline?
a) Well, if 1.0 g of gasoline releases 11 kcal of heat, then 3.0 g of gasoline would release 33 kcal. To convert kcal to megajoules, we need to divide by 4.184 (since 1 kcal = 4.184 MJ). So, 33 kcal ÷ 4.184 = 7.88 MJ. So, when 3.0 g of gasoline burns, it releases approximately 7.88 megajoules of heat.
b) Now, let's figure out how many hours the television can run on the energy provided by 3.0 g of gasoline. We know that the television requires 150 kJ/h to run. However, we need to convert the 3.0 g of gasoline to liters because density is given in g/mL.
Given that, the density of gasoline is 0.74 g/mL, we can calculate the volume of gasoline in liters as follows:
3.0 g ÷ 0.74 g/mL = 4.05 mL.
Therefore, the television can run on the energy provided by 3.0 g of gasoline for 4.05 mL of gasoline. Now, we need to figure out how many hours this amount of gasoline can power the television for.
To do that, we'll use the fact that 1 g of gasoline is equivalent to 11 kcal of heat. We also know that 1 kcal is equivalent to 4.184 kJ. Therefore, 1 g of gasoline is equivalent to 11 x 4.184 kJ.
Now, let's calculate the total energy in kilojoules provided by 3.0 g of gasoline:
3.0 g x 11 x 4.184 kJ = 139.092 kJ.
Finally, let's divide the total energy provided by the gasoline (139.092 kJ) by the energy required by the television per hour (150 kJ/h) to find out how many hours the television can run:
139.092 kJ ÷ 150 kJ/h = 0.927 hours.
So, the television can run for approximately 0.927 hours on the energy provided by 3.0 g of gasoline.
To solve these problems, we need to convert the given units to a consistent unit of energy like megajoules (MJ).
First, let's convert the heat released (given in kcal) to megajoules (MJ).
1 kcal = 4.184 kJ
1 MJ = 1000 kJ
a) How many megajoules are released when 3.0 g of gasoline burns?
To find this, we can set up a proportion:
(11 kcal / 1 g) = (x MJ / 3.0 g)
Cross-multiplying and solving for x, we get:
x = (11 kcal * 3.0 g) / 1 g
x = 33 kcal
Now, let's convert kcal to MJ:
33 kcal = 33 kcal * (4.184 kJ / 1 kcal) = 138.012 kJ
Finally, converting kJ to MJ:
138.012 kJ = 138.012 kJ / 1000 kJ = 0.138012 MJ
Therefore, 3.0 g of gasoline burns to release approximately 0.138012 MJ of heat.
b) Now let's calculate how many hours the television can run on the energy provided by 3.0 g of gasoline.
To find this, we need to know the energy consumption rate in kilojoules per hour (kJ/h).
150 kJ/h = 150 kJ/h * (1 MJ / 1000 kJ) = 0.150 MJ/h
Now, we divide the total energy provided by 3.0 g of gasoline (0.138012 MJ) by the energy consumption rate per hour (0.150 MJ/h):
(0.138012 MJ) / (0.150 MJ/h) = 0.92008 h
Therefore, the television can run approximately for 0.92008 hours, or about 55 minutes, on the energy provided by 3.0 g of gasoline.
To solve these problems, we need to convert the given information to a consistent unit and apply the appropriate formulas. Let's go through each question step by step:
a) How many megajoules are released when 3.0 g of gasoline burns?
To find the amount of energy released in megajoules, we need to convert the given energy in kcal to kJ. Remember that 1 kcal is equal to 4.184 kJ.
Given:
- 1.0 g of gasoline releases 11 kcal of heat
- Density of gasoline is 0.74 g/mL
First, we need to find the volume of gasoline that corresponds to 3.0 g using the density formula:
density = mass / volume
volume = mass / density
volume = 3.0 g / 0.74 g/mL = 4.054 mL (rounded to three significant figures)
Next, we need to convert the volume to grams since we know the energy released for 1 g of gasoline:
1.0 g of gasoline releases 11 kcal
Therefore, 4.054 g of gasoline would release (4.054 g) * (11 kcal / 1 g) = 44.594 kcal
Now, we can convert kcal to kJ:
44.594 kcal * (4.184 kJ / 1 kcal) = 186.483 kJ (rounded to three significant figures)
Finally, let's convert kJ to megajoules by dividing by 1000:
186.483 kJ / 1000 = 0.186483 MJ (rounded to three significant figures)
Therefore, when 3.0 g of gasoline burns, it releases approximately 0.186 MJ of heat.
b) If a television requires 150 kJ/h to run, how many hours can the television run on the energy provided by 3.0 g of gasoline?
We already calculated that 3.0 g of gasoline releases 186.483 kJ of heat. Now, we need to find the number of hours the television can run using this energy.
Given:
- Energy provided by 3.0 g of gasoline = 186.483 kJ
- Power required to run the television = 150 kJ/h
We can use the formula Power = Energy / Time to find the time.
Time = Energy / Power
Time = 186.483 kJ / 150 kJ/h
Time = 1.243 hours (rounded to three decimal places)
Therefore, the television can run for approximately 1.243 hours on the energy provided by 3.0 g of gasoline.