A container holds a fixed mass of gas. The gas is compressed until its volume is reduced in the ratio 5 : 2. Compared to its initial value, the density of the gas becomes ______.
2.5ρ
Density is \(\rho = \frac{m}{V}\); the mass of gas is fixed, so density is inversely proportional to volume.
Volume reduced in the ratio 5 : 2 means \(V_2 = \frac{2}{5}V_1\).
\(\rho' = \frac{m}{\frac{2}{5}V_1} = \frac{5}{2}\rho = 2.5\rho\)
Hence, the answer is 2.5ρ.
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