When 1.0g of gasoline burns, it releases 11 kcal. The density of gasoline is 0.74 g/mL.
a. How many megajoules are released when 1.0 gal 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 1.0 gal of gasoline?
Can someone please show me how to solve this problem? I have no idea how to even begin.
(a) 1.0gal * 3785mL/gal * 0.74g/mL * 11kcal/g * 4.184kJ/kcal = ___ kJ
(b) divide the kJ from (a) by 150 to get hours
If you watch the units, the conversions will take care of themselves.
Well, solving problems can be a bit like driving a car. Don't worry, I'll be your GPS and guide you through this problem!
First, let's tackle part (a) of the problem.
a. How many megajoules are released when 1.0 gal of gasoline burns?
To find this, we need to find out how many grams of gasoline are in 1.0 gallon.
Given that the density of gasoline is 0.74 g/mL and there are 1,000 mL in a liter, we can convert from gallons to liters using the conversion factor:
1.0 gal * (3.78541 L / 1 gal) = 3.78541 L
Now, we can find the mass of gasoline in grams:
3.78541 L * (0.74 g/mL) = 2.8 g
Next, we use the 11 kcal released per gram of gasoline:
2.8 g * (11 kcal / 1 g) = 30.8 kcal
Lastly, we convert kcal to megajoules:
30.8 kcal * (4.184 kJ / 1 kcal) * (1 MJ / 1,000 kJ) = 0.129 MJ
Therefore, when 1.0 gal of gasoline burns, it releases approximately 0.129 megajoules of energy.
Now onto part (b)!
b. If a television requires 150 kJ/h to run, how many hours can the television run on the energy provided by 1.0 gal of gasoline?
We already know from part (a) that 1.0 gal of gasoline releases 0.129 MJ of energy.
Since 1 MJ = 1,000 kJ, we convert it to kJ:
0.129 MJ * (1,000 kJ / 1 MJ) = 129 kJ
Now we can find the number of hours the television can run:
129 kJ / 150 kJ/h = 0.86 h
So, the television can run for approximately 0.86 hours on the energy provided by 1.0 gal of gasoline.
And there you have it! Problem solved with a touch of humor along the way. Remember, if you have any more questions, I'm here to assist you. Drive safely!
To solve this problem, we need to use the given information to find the total energy released by 1.0 gallon of gasoline when it burns, and then determine how many hours the television can run on this energy.
Step 1: Find the mass of 1.0 gallon of gasoline
The given density of gasoline is 0.74 g/mL. Since 1 gallon is equivalent to 3.785 liters, we can convert this to grams by multiplying:
Mass of gasoline = Density x Volume = 0.74 g/mL x 3785 mL = 2801.9 g
Step 2: Find the energy released by 1.0 g of gasoline
Given that 1.0 g of gasoline releases 11 kcal, we can convert this to joules by multiplying:
1 kcal = 4.184 kJ
Energy released by 1.0 g of gasoline = 11 kcal x 4.184 kJ/kcal = 46.024 kJ
Step 3: Find the energy released by 1.0 gallon of gasoline
To find the total energy released by 1.0 gallon of gasoline, we can multiply the energy released by 1.0 g of gasoline by the mass of 1.0 gallon of gasoline:
Energy released by 1.0 gallon of gasoline = Energy released by 1.0 g of gasoline x Mass of gasoline
= 46.024 kJ/g x 2801.9 g
= 128,850.58 kJ
Step 4: Find the number of hours the television can run on the energy provided by 1.0 gallon of gasoline
Given that the television requires 150 kJ/h to run, we can divide the total energy released by 1.0 gallon of gasoline by the energy required to determine the number of hours the television can run:
Number of hours = Energy released by 1.0 gallon of gasoline / Energy required by the television
= 128,850.58 kJ / 150 kJ/h
≈ 859.004 hours (rounded to the nearest whole number)
Answer:
a. 1.0 gallon of gasoline releases approximately 128,850.58 kJ of energy.
b. The television can run for approximately 859 hours using the energy provided by 1.0 gallon of gasoline.
To solve this problem, we need to use the given information and some conversion factors. Let's break down the problem step by step:
a. How many megajoules are released when 1.0 gal of gasoline burns?
First, we need to convert the volume from gallons to milliliters (mL) because the density of gasoline is given in g/mL.
1 gallon = 3.78541 liters
1 liter = 1000 milliliters
Therefore, 1 gallon = 3.78541 * 1000 = 3785.41 mL
Next, we need to find the mass of 1 gallon of gasoline. Given that the density of gasoline is 0.74 g/mL, we can use the following formula:
Mass = density x volume
Mass = 0.74 g/mL x 3785.41 mL = 2800.09 g
Now, using the information that 1.0g of gasoline releases 11 kcal of energy, we can calculate the energy released by 1 gallon of gasoline:
Energy = (Mass of gasoline x Energy released per gram) / 1000
Energy = (2800.09 g x 11 kcal/g) / 1000 = 30.80199 kcal
Lastly, we need to convert the energy from kilocalories to megajoules:
1 kilocalorie = 4.184 joules
1 megajoule = 10^6 joules
Energy = 30.80199 kcal x 4.184 J/kcal / 10^6 = 0.12854 MJ
Therefore, 1.0 gallon of gasoline releases approximately 0.12854 megajoules of energy when burned.
b. If a television requires 150 kJ/h to run, how many hours can the television run on the energy provided by 1.0 gallon of gasoline?
To calculate the number of hours the television can run on the energy provided by 1.0 gallon of gasoline, we can use the formula:
Number of hours = Energy provided by gasoline / Energy required per hour
Number of hours = 0.12854 MJ / 150 kJ/h
Before calculating, we need to convert kilojoules to megajoules:
1 megajoule = 1000 kilojoules
Energy required per hour = 150 kJ/h / 1000 = 0.15 MJ/h
Now, we can calculate the number of hours:
Number of hours = 0.12854 MJ / 0.15 MJ/h ≈ 0.85693 hours
Therefore, the television can run for approximately 0.85693 hours (or about 51.4 minutes) on the energy provided by 1.0 gallon of gasoline.