Question

The mean value of the coefficient of real expansion of mercury is 18.2 * 10^{-5 o}C^-1​. Density of mercury at 20 ^oC is 13.55 g/cc. At what higher temperature, will the error in the measurement of density be 1%? [answer is 74.94 ^oC]
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Answer 1

Dear Student
as the temperature changes the density also changes from formula

$$\begin{gathered} {\rho }_{T_2}=\frac{{\rho }_{T_1}}{1+\gamma ∆T}(here{\rho }_{T_2}isfinaldensityand{\rho }_{T_1}isinitialdensityandischangeintemp) \\ \frac{{\rho }_{T_2}}{{\rho }_{T_1}}=\frac{1}{1+\gamma ∆T} \\ (\frac{{\rho }_{T_2}}{{\rho }_{T_1}}-1)\times 100=(\frac{1}{1+\gamma ∆T}-1)\times 100 \\ 1=\left(\frac{1-1-\gamma ∆T}{1+\gamma ∆T}\right)\times 100 \\ 1=\frac{-\gamma ∆T}{1+\gamma ∆T})\times 100(-vesignindicatesdensitydecreases) \\ 1=\frac{-\gamma ∆T}{1+\gamma ∆T})\times 100 \\ solvingaboveeq \\ ∆T=\frac{1}{99\gamma } \\ {T}_{final}-20=55.55 \\ {T}_{final}=75.{55}^{0}C \end{gathered}$$
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