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10-1.Thermometry, Thermal Expansion and Calorimetry
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The figure shows a glass tube (linear co-efficient of expansion is $\alpha$) completely filled with a liquid of volume expansion co-efficient $\gamma$. On heating length of the liquid column does not change. Choose the correct relation between $\gamma$ and $\alpha$
A
$\gamma=\alpha$
B
$\gamma= 2\alpha$
C
$\gamma= 3\alpha$
D
$\gamma = \frac{\alpha }{3}$
Solution
(b) When length of the liquid column remains constant, then the level of liquid moves down with respect to the container, thus $\gamma$ must be less than $3\alpha$.
Now we can write $V = V_0(1 + \gamma \Delta T)$
Since $V = Al_0 = [A_0 (1 + 2\alpha \Delta T)]l_0 = V_0 (1 + 2\alpha \Delta T)$
Hence $V_0(1 + \gamma \Delta T) = V_0(1 + 2\alpha \Delta T) ==> \gamma= 2\alpha$ .
Standard 11
Physics
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