Properties Of Solids And Liquids Question 423
Question: A horizontal tube, open at both ends, contains a column of liquid. The length of this liquid column does not change with temperature. Let $ \gamma $ = coefficient of volume expansion of the liquid and $ \alpha $ = coefficient of linear expansion of the material of the tube, then
Options:
A) $ \gamma =\alpha $
B) $ \gamma =2\alpha $
C) $ \gamma =3\alpha $
D) $ \gamma =0 $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Let $ A _{0} $ and At be the areas of cross-section of the tube at temperature 0 and t respectively, 1 = length of the liquid column (constant) $ V _{0} $ and $ V _{t} $ be the volumes of the liquid at temperature 0 and t respectively, $ V _{0}=\ell A _{0}V _{t}=\ell A _{t} $
$ {{V} _{t}}=V _{0}( l+\gamma t )A _{t}=A _{0}( l+2\alpha t ) $
$ \therefore V _{t}=\ell A _{0}( l+2\alpha t )=V _{0}( l+\gamma t ) $
$ =\ell A _{0}( l+\gamma t )or\gamma =2a. $
