A cylindrical gas bottle has internal dimensions of 18cm in diameter and 49cm in height. It is designed to contain compressed oxygen gas. The bottle has a mass of 1.75kg when empty and 3.15kg when full of oxygen gas. What is the density of the oxygen gas in a full bottle in kg/m^3?
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Volume of oxygen gas
$V = \frac{1}{4}\pi (\frac{18}{100})^2 (\frac{49}{100}) = 0.003969\pi ~ \text{ m}^3$
Mass of oxygen gas
$m = 3.15 - 1.75 = 1.4 ~ \text{ kg}$
Density of oxygen gas
$\rho = \dfrac{m}{V} = \dfrac{1.4}{0.003969\pi} = 112.28 ~ \text{ kg/m}^3$
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