Answer:
The average density of the full gas can is [tex]874~Kg~m^{-3}[/tex], assuming the standard density of gasoline to be [tex]748.9~Kg~m^{-3}[/tex].
Explanation:
Given the mass of the can ([tex]m_{C}[/tex]) is 2.5 Kg and the volume (V) occupied by gasoline is 20 L. Assuming the standard density of gasoline ([tex]\rho_{g}[/tex]) to be 748.9 [tex]Kg~m^{-3}[/tex], if '[tex]m_{g}[/tex]' be the mass of the gasoline occupied in the entire can, then
[tex]m_{g} = \rho_{g} \tomes V = 748.9 Kg~m^{-3} \times 20~L = 748.9 Kg~m^{-3} \times 20 \times 10^{-3}~m^{3} = 14.98 Kg[/tex]
If '[tex]\rho[/tex]' be the average density of the full gas can, then
[tex]\rho = \dfrac{Total~mass}{Total~volume} = \dfrac{m_{C} + m_{g}}{V} = \dfrac{(2.5 + 14.98)~Kg}{20 \times 10^{-3}~m^{3}} = 874~Kg~m^{-3}[/tex]
A 2.50-kg steel gasoline can holding 20.0 L of gasoline has an average density of 0.875 kg/L.
A 2.50-kg steel gasoline can holds 20.0 L (V) of gasoline when full.
Since the density of gasoline is 0.7489 kg/L, the mass (m(g)) of 20.0 L of gasoline is:
[tex]m(g) = 20.0 L \times \frac{0.7489kg}{L} = 15.0 kg[/tex]
The total mass (m) will be the sum of the mass of the steel can (m(s)) and the mass of the gasoline (m(g)).
[tex]m = m(s) + m(g) = 2.50 kg + 15.0 kg = 17.5 kg[/tex]
The average density (ρ) will be the ratio of the total mass (m) to the total volume (V).
[tex]\rho = \frac{m}{V} = \frac{17.5kg}{20.0L} = 0.875kg/L[/tex]
A 2.50-kg steel gasoline can holding 20.0 L of gasoline has an average density of 0.875 kg/L.
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