Properties Of Solids And Liquids Question 417
Question: The density of water at $ 4{}^\circ C $ is$ 1000.0 kg/m^{3} $ and at $ 100{}^\circ C $ it is $ 958.4 kg/m^{3} $ . The cubic expansively of water between these temperatures is
Options:
A) $ 4.5\times {{10}^{-3}}/K $
B) $ 5.4\times {{10}^{-5}}/K $
C) $ 4.5\times {{10}^{-4}}/K $
D) $ 5.4\times {{10}^{-6}}/K $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ V=V _{0}(1+ \alpha \Delta \theta ) $ where $ \Delta \theta $ is the difference in temperature, $ \alpha $ is the coefficient of volume expansion. i.e., $ \frac{V-V _{0}}{V _{0}}\frac{1}{\Delta \theta }=\alpha $
$ \alpha =\frac{\frac{m}{d _{2}}-\frac{m}{d _{1}}}{m/d _{1}}.\frac{1}{\Delta \theta }=\frac{( d _{1}-d _{2} )}{( d _{1}d _{2} )}\times \frac{d _{1}}{\Delta \theta } $
$ =\frac{( d _{1}-d _{2} )}{( d _{1}d _{2} )}.\frac{d _{1}}{\Delta \theta }=\frac{1000-958.4}{958.4\times 96} $
$ =4.5\times l{{0}^{-4}} $ per degree K.
