Question

A specific gravity bottle contains m grams of liquid of apparent expansion ${\gamma }_a$ at 0${}^0$C. When it is heated to t${}^0$ C the mass of liquid expelled is :

• A. $\frac{1+{\gamma }_{a}t}{{\gamma }_{a}mt}$
• B. $\frac{{\gamma }_{a}m}{1+{\gamma }_{a}t}$
• C. $\frac{{\gamma }_{a}mt}{1+{\gamma }_{a}t}$
• D. $\frac{{\gamma }_{a}mt}{1-{\gamma }_{a}t}$

Answer 1

Answer: (C)

$\frac{{\gamma }_{a}mt}{1+{\gamma }_{a}t}$

${\gamma }_a=\frac{x}{(m-x)\Delta T}$
$\Rightarrow x+{\gamma }_{a}x\Delta T={\gamma }_{a}m\Delta T$
$\Rightarrow x(1+{\gamma }_a\Delta T)={\gamma }_{a}m\Delta T$
$\Rightarrow x=\frac{{\gamma }_{a}m\Delta T}{1+{\gamma }_a\Delta T}$