A solid metal block and a gas enclosed in a flexible balloon are subjected to the same increase in external pressure. Which one experiences the greater increase in density?
The gas inside the balloon
Density is \(\rho = \frac{m}{V}\); for a fixed mass, the density rises only if the volume falls.
Solids are nearly incompressible: their atoms are tightly packed and their bulk modulus is very large, so a pressure increase produces a negligible change in volume and density.
A gas has large intermolecular spaces and is highly compressible (Boyle’s law, \(PV\) = constant at fixed temperature), so the same pressure rise reduces its volume noticeably and its density increases much more.
The other options fail: density does change for the gas; the changes are not equal because compressibilities differ enormously; and the solid’s change is the smaller one.
Hence, the answer is The gas inside the balloon.
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