Question

A 2.5 kg steel gasoline tank can holds 20.0 L of gasoline when full. What is the average density (in Kg/m^3) of the full gas can, taking into account the volume occupied by steel as well as by gasoline? Take the density of gasoline as 680.0 kg/m^3 and the density of steel as 7800.0 kg/m3. Note: 1L =.001m^3.

Answer 1

Answer:

$D=792.3\ kg/m^3$

Explanation:

Average Density

The density of an object of mass m and volume V is

$\displaystyle D=\frac{m}{V}$

If we know the density and the volume occupied by the object, the mass can be computed as

$m=D.V$

The tank can hold 20 L of gasoline when full. Converting to cubic meters

$V_g=20*0.001=0.02\ m^3$

That's the volume of the gasoline it contains. Knowing the density of the gasoline, we get the mass of gasoline.

$m_g=680*0.02=13.6\ kg$

To know the total mass of both, we add the 2.5 kg of the tank

$m=m_t+m_g=13.6+2.5=16.1\ kg$

The volume of the tank is computed solving for V

$\displaystyle V=\frac{m}{D}$

$\displaystyle V_t=\frac{2.5}{7800}=3.205\times 10^{-4}\ m^3$

The total volume is

$V=V_g+V_t=0.02+3.205\times 10^{-4}=0.0203\ m^3$

The average density is

$\displaystyle D=\frac{16.1}{0.0203}$

$\boxed{D=792.3\ kg/m^3}$