Question

A fluid having a thermal coefficient of volume expansion $\gamma $ is filled in a cylindrical vessel up to a height $h_{0}$ . The coefficient of linear thermal expansion of the material of the vessel is $\alpha $ . If the fluid is heated with the vessel, then find the level of liquid when the temperature increases by $\Delta \theta $ .

• A. $\frac{h_{0} \left(\right. 1 + γΔ\theta \left.\right)}{\left(\right. 1 + 2 αΔ\theta \left.\right)}$
• B. $\frac{h_{0} \left(\right. 1 + γΔ\theta \left.\right)}{\left(\right. 1 + 3 αΔ\theta \left.\right)}$
• C. $\frac{h_{0} \left(\right. 1 + γΔ\theta \left.\right)}{\left(\right. 1 + αΔ\theta \left.\right)}$
• D. $h_{0}\left(\right. 1 + γΔ\theta \left.\right)$

Answer 1

Answer: (A)

$A_{base}=A_{0}\left(1 + βΔ T\right)=A_{0}\left(\right.1+2αΔ\theta \, \left.\right)$
$V_{fluid}=V_{0}\left(1 + γΔ T\right)=A_{0}h_{0}\left(\right.1+γΔ\theta \left.\right)$
$Ah=A_{0}\left(1 + 2 αΔ\theta \right)h=A_{0}h_{0}\left(\right.1+γΔ\theta \left.\right)$
$h=\frac{h_{0} \left(\right. 1 + γΔ\theta \left.\right)}{\left(\right. 1 + 2 αΔ\theta \left.\right)}$