Question

the density of steel at 0° is 8.0g/cc. at what temperature is density lesser by 0.1%. coefficient of linear thermal expansion is 10^-5+°c

Answer 1

Dear Student
$$\begin{gathered} Usetheformulaofvolumetricthermalexpansion, \\ V=V₀(1+3\alpha \times ∆T)because,Y=3\alpha \\ weknow,density=mass/Volume, \\ becausemasscan\text{'}tbechangeiftemperaturechange. \\ so,formulaofthermalexpansionfordensity, \\ d=d₀(1+3\alpha \times ∆T) \\ d=d₀-0.1\%\times d₀ \\ d=d₀(1-0.001) \\ 0.999\times d₀=d₀(1+3\alpha \times ∆T) \\ 0.999=(1+3\alpha \times ∆T) \\ -0.001=3\alpha \times ∆T \\ -0.001=3\alpha (T-0) \\ Given\alpha ={10}^{-5}/°C \\ -{10}^{-3}=3\times {10}^{-5}\times T \\ -100=3\times T \\ T=\frac{-100}{3}=-33.33°C \end{gathered}$$
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