A 2.60 kg steel gas can holds 15.0 L of gasoline when full. What is the average density(kg/m^3)of the full gas can, taking into account the volume occupied by steel as well as by gasoline?
Gasoline density ~0.74 Kg/Liter
so
Weight of 15liter gasoline = 11.10 Kg
Weight of steel can = 02.60 Kg
Total weight = 13.70 Kg
01 Liter of gasoline=0.001 m^3
so
15 liter of gasoline=0.001*15
=0.015 m^3
so
Density =mass/volume
=13.70/0.015
=913.33 Kg/m^3
Vol of steel has not been accounted in this calculation. Kindly check.
To find the average density of the full gas can, we need to calculate the total mass and total volume of both the steel and the gasoline, and then divide the mass by the volume.
1. Calculate the mass of the steel:
The density of steel is typically around 7850 kg/m^3. Since the gas can has a mass of 2.60 kg, we can calculate the volume of the steel using the formula:
mass = density * volume.
Rearranging the formula gives us:
volume = mass / density.
Plugging in the values gives us:
volume = 2.60 kg / 7850 kg/m^3.
Calculating that gives us:
volume = 0.000331528 m^3.
2. Calculate the volume of the gasoline:
We are given that the gas can holds 15.0 L of gasoline. To convert this to cubic meters, we need to multiply by the conversion factor:
1 L = 0.001 m^3.
So, the volume of the gasoline is:
volume = 15.0 L * 0.001 m^3/L.
Calculating that gives us:
volume = 0.015 m^3.
3. Calculate the total volume of the gas can:
To find the total volume of the gas can, we need to add the volumes of the steel and the gasoline:
total volume = volume of steel + volume of gasoline.
Plugging in the values gives us:
total volume = 0.000331528 m^3 + 0.015 m^3.
Calculating that gives us:
total volume = 0.015331528 m^3.
4. Calculate the total mass of the gas can:
To find the total mass, we simply add the mass of the steel and the mass of the gasoline:
total mass = mass of steel + mass of gasoline.
Plugging in the values gives us:
total mass = 2.60 kg + mass of gasoline.
5. Calculate the density of the gas can:
Finally, we can calculate the density by dividing the total mass by the total volume:
density = total mass / total volume.
However, we need to find the mass of the gasoline first. We know that the volume of the gasoline is 15.0 L, and the density of gasoline is typically around 740 kg/m^3. We can calculate the mass of the gasoline using the formula:
mass = density * volume.
Plugging in the values gives us:
mass of gasoline = 740 kg/m^3 * 0.015 m^3.
Calculating that gives us:
mass of gasoline = 11.1 kg.
Now, we can calculate the density of the gas can:
density = (2.60 kg + 11.1 kg) / 0.015331528 m^3.
Calculating that gives us:
density = 843.68 kg/m^3.
Therefore, the average density of the full gas can, taking into account the volume occupied by steel as well as by gasoline, is approximately 843.68 kg/m^3.
To find the average density of the full gas can, we need to consider the volume occupied by both the steel and the gasoline.
The total volume of the gas can is given as 15.0 L. However, this volume includes the steel and the gasoline. We need to find the volume occupied by each component individually.
First, let's convert the volume of the gas can to cubic meters (m^3). There are 1000 liters in a cubic meter, so:
Volume of gas can = 15.0 L = 15.0 / 1000 = 0.015 m^3
Now, we can calculate the volume occupied by the steel. The mass of the steel gas can is given as 2.60 kg. To find the volume of an object, we can use the formula:
Volume = Mass / Density
The density of steel can vary, but for the purpose of this calculation, let's assume the average density of steel is 7850 kg/m^3.
Volume of steel = 2.60 kg / 7850 kg/m^3 = 0.00033 m^3 (rounded to 5 decimal places)
Next, we need to subtract the volume occupied by the steel from the total volume of the gas can to find the volume occupied by the gasoline.
Volume of gasoline = Total volume of gas can - Volume of steel
= 0.015 m^3 - 0.00033 m^3
= 0.01467 m^3 (rounded to 5 decimal places)
Finally, the average density is calculated by dividing the total mass (steel + gasoline) by the total volume (steel + gasoline):
Average density = (Mass of steel + Mass of gasoline) / (Volume of steel + Volume of gasoline)
= (2.60 kg + Mass of gasoline) / (0.00033 m^3 + 0.01467 m^3)
= 2.60 kg / 0.01467 m^3
= 177.22 kg/m^3 (rounded to 2 decimal places)
Therefore, the average density of the full gas can, taking into account the volume occupied by the steel as well as by gasoline, is 177.22 kg/m^3.