WBCS Preliminary Examination 2023 — General Studies · Question 188 of 200

Answer: (D) volume

For a temperature rise $\Delta T$, the fractional increase in length (or diameter) is $\alpha\Delta T$, in surface area $2\alpha\Delta T$ and in volume $3\alpha\Delta T$, because area depends on the square and volume on the cube of the linear dimension. The percentage increases are therefore in the ratio 1 : 2 : 3, and volume changes the most. Density does not increase at all: the mass is unchanged while the volume grows, so density falls by about $3\alpha\Delta T$. For iron, $\alpha$ is about $1.2\times10^{-5}$ per °C.