Properties Of Solids And Liquids Question 420

Question: The density of steel at $ 0 {}^\circ C $ is 8.0 g/cc. At what temperature is density lesser by 0.1%? Coefficient of linear expansion of steel is $ 1{{0}^{-5}} /{}^\circ C $ .

Options:

A) $ 37.2{}^\circ C $

B) $ 33.3{}^\circ C $

C) $ 55.4{}^\circ C $

D) $ 40.2{}^\circ C $

Show Answer

Answer:

Correct Answer: B

Solution:

[b] $ \rho =\frac{{\rho _{0}}}{1+\gamma \Delta \theta }\cong {\rho _{0}}( 1-\gamma \Delta \theta );\frac{\Delta \rho }{\rho }=-\gamma \Delta \theta $

$ \frac{1}{100}=3\times {{10}^{-5}}\Delta \theta ;\Delta \theta =\frac{100}{3}={{33.3}^{o}}C $



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