Question

The density of liquid gallium at ${30}^o$C is $6.095$ g/mL. Because of its wide liquid range ($30$ to ${2400}^o$C), gallium could be used as a barometer fluid at high temperature. What height (in cm) of gallium will be supported on a day when the mercury barometer reads $740$ torr? (The density of mercury is $13.6$g/mL).

• A. $322$
• B. $285$
• C. $165$
• D. $210$

Answer 1

The correct option is C $165$

Density of liquid gallium $=6.095g/mL$

$T={30}^{\circ }C$

We need to find height (in cm) of gallium when barometer of mercury reads 740 torr. Let height be ."h" cm

We know that:

$\begin{array}{cc}P& =\rho gh\\ where:g=& 9.8m/s^2\end{array}$

$P=740torr=98,658.28pa$

$\left\{\begin{array}{c}1\text{torr}=133.32\text{pa}\\ \therefore 740\text{torr}=740\times 133.32=98,658.28pa\end{array}\right\}$

$\text{putting in values, we get:}$

$98,658\cdot 28=6095\frac{kg}{m^2}\times 9.8\frac{m}{s^2}\times h$

$\text{solving for h, we get:}$

$$\begin{array}{cc}h& =\frac{98658\cdot 28}{6095\times 9.8}m\\ h& =1.65m\\ & h=165cm\end{array}$$