A 2.60 kg steel gas can holds 15.0 L of gasoline when full. What is the average density(kg/m^2))of the full gas can, taking into account the volume occupied by steel as well as by gasoline?
Steel ρ₁ =7800 kg/m³
V₁=m₁/ρ₁=2.6/7800 = 3.3•10⁻⁴ m³
Gasoline ρ₂ = 750 kg/m³
m₂=ρ₂V₂=750•15•10⁻³ =11.25 kg
ρ(ave) =( m₁+m₂)/(V₁+V₂) =
=(2.6+11.25)/ (3.3•10⁻⁴+15•10⁻³) =
=13.85/0.01503=921 kg/m³
The final answer depends on the reference values of densities:
the density of gasoline ρ = 700 – 770 kg/m³ and the density of steel
ρ = 7400 – 8000 kg/m³
To find the average density of the full gas can, you need to consider both the volume occupied by steel and the volume occupied by gasoline.
First, calculate the volume of the steel can. You are given that the can holds 15.0 L of gasoline, so the volume of the steel can is also 15.0 L.
Next, convert the volume of the steel can and the volume of gasoline to cubic meters. 1 L is equal to 0.001 cubic meters, so the volume of the steel can and gasoline is both 0.015 cubic meters.
Now, calculate the mass of the steel can. You are given that the mass of the can is 2.60 kg.
The density of a substance is defined as mass divided by volume. So, you can find the density of the steel can using the formula:
Density = Mass / Volume
Density of the steel can = 2.60 kg / 0.015 m³
Now, add the density of the steel can to the density of gasoline. The density of gasoline is approximately 0.75 kg/L.
First, convert the density of gasoline to kg/m³ by multiplying by 1000:
Density of gasoline = 0.75 kg/L * 1000 L/m³ = 750 kg/m³
Now, add the densities:
Average density = Density of steel can + Density of gasoline
Therefore, the average density of the full gas can is:
Average density = (2.60 kg / 0.015 m³) + 750 kg/m³
Calculate this to get the final answer.