Your friend Zach can inhale to create a gauge pressure of -70 mm of Hg (density of Hg = 13.6 g/cm³).The height of water (density of water = 1 g/cm³)Zach can raise in a straw is A)95.2 cm. B)66.2 cm. C)45.9 cm. D)32.1 cm. E)19.2 cm.

Question

Quizplus · Accepted Answer

The height of the water column that can be raised in a straw by creating a vacuum is determined by equating the pressure due to the column of water to the gauge pressure created by inhaling. The gauge pressure $P$ is given by $P = \rho_{\text{Hg}} \cdot g \cdot h_{\text{Hg}}$, where $\rho_{\text{Hg}}$ is the density of mercury, $g$ is the acceleration due to gravity, and $h_{\text{Hg}}$ is the height of the mercury column. To find the height of the water column $h_{\text{water}}$, we use the formula $P = \rho_{\text{water}} \cdot g \cdot h_{\text{water}}$.Given that $\rho_{\text{Hg}} = 13.6 \, \text{g/cm}^3 = 13600 \, \text{kg/m}^3$, $h_{\text{Hg}} = 70 \, \text{mm} = 0.07 \, \text{m}$, and $\rho_{\text{water}} = 1 \, \text{g/cm}^3 = 1000 \, \text{kg/m}^3$, we can equate the pressures to solve for $h_{\text{water}}$:$$13600 \cdot 9.8 \cdot 0.07 = 1000 \cdot 9.8 \cdot h_{\text{water}}$$Solving for $h_{\text{water}}$, we get:$$h_{\text{water}} = \frac{13600 \cdot 0.07}{1000} = 0.952 \, \text{m} = 95.2 \, \text{cm}$$Therefore, Zach can raise water to a height of 95.2 cm in a straw.

Your Friend Zach Can Inhale to Create a Gauge Pressure