Question

The apparatus shown in the figure consists of four glass columns connected by horizontal sections. The height of two central columns $B\&C$ are $46cm$ each. The two outer columns $A\&D$ are open to the atmosphere. $A\&C$ are maintained at a temperature of ${95}^{o}C$ while the columns $B\&D$ are maintained at $5^{o}C.$ The height of the liquid in $A\&D$ measured from the base line are $58.8cm\&51cm$ respectively. Determine the coefficient of thermal expansion of the liquid.

Answer 1

According to pascal's law

$p=p_0+e_{A}g{h}_A-e_{B}g{h}_B+e_{C}g{h}_C-e_{D}g{h}_D$

$\Rightarrow \frac{p_5^{\circ }c}{p_{95}^{\circ }c}=\frac{52.8+49}{49+51}=1.08$

$r=\frac{V_{95}-V_5}{V_5(95-5)}=\left(\frac{p_s-p_{95}}{e_{95}\times 90}\right)$

$(\frac{p_5}{p_{95}}-1)\frac{1}{90}=2\times {10}^{-4}$ ${}^{\circ }C$

$\frac{r}{3}=6.1\times {10}^{-5}/C$