Variation of Density with Temperature
Category : JEE Main & Advanced
Most substances (solid and liquid) expand when they are heated, i.e., volume of a given mass of a substance increases on heating, so the density should decrease \[\left( \text{as }\rho \propto \frac{1}{V} \right)\]. For a given mass
\[\rho \propto \frac{1}{V}\] \[\Rightarrow \]\[\frac{{{\rho }'}}{\rho }=\frac{V}{{{V}'}}=\frac{V}{V+\Delta V}=\frac{V}{V+\gamma V\Delta \theta }=\frac{1}{1+\gamma \,\Delta \theta }\]
\[\Rightarrow \]\[{\rho }'=\frac{\rho }{1+\gamma \,\Delta \theta }=\rho \,{{(1+\gamma \,\Delta \theta )}^{-1}}=\rho \,(1-\gamma \,\Delta \theta )\]
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