Question

1. why is the fluid in a barometer mercury, rather than water or another liquid?
2. explain why you cannot use a pump like the one at the right to lift water up to the 3rd floor of an apartment complex.
3. one standard atmosphere of pressure (sp) is equivalent to ____ mmhg
4. use the appropriate unit - relationship to convert these pressure measurements from one system of units to another. see pressure unit equivalencies shown below

760 mmhg = 14.7 psi (pounds per square inch) = 101.3 kpa
a. 320 mmhg x __ = __ kpa
b. 30.0 psi x __ = __ mmhg
c. the barometric pressure in breckenridge, colorado (elevation 9600 feet) is 77.3 kpa. how many mm hg is this?

Explanation:

Step1: Recall pressure - unit conversion

We know that $760\ mmHg = 101.3\ kPa$.

Step2: Convert 320 mmHg to kPa

Set up a proportion: $\frac{320\ mmHg}{x\ kPa}=\frac{760\ mmHg}{101.3\ kPa}$. Cross - multiply gives $760x = 320\times101.3$. Then $x=\frac{320\times101.3}{760}\approx42.9\ kPa$.

Step3: Recall pressure - unit conversion for psi and mmHg

We know that $760\ mmHg = 14.7\ psi$.

Step4: Convert 30.0 psi to mmHg

Set up a proportion: $\frac{y\ mmHg}{30.0\ psi}=\frac{760\ mmHg}{14.7\ psi}$. Cross - multiply gives $14.7y = 30.0\times760$. Then $y=\frac{30.0\times760}{14.7}\approx1551\ mmHg$.

Step5: Convert 77.3 kPa to mmHg

Set up a proportion: $\frac{z\ mmHg}{77.3\ kPa}=\frac{760\ mmHg}{101.3\ kPa}$. Cross - multiply gives $101.3z = 77.3\times760$. Then $z=\frac{77.3\times760}{101.3}\approx579\ mmHg$.

Step6: Answer question 5

Mercury is used in barometers because of its high density. The density of mercury ($
ho_{Hg}=13.6\ g/cm^{3}$) is much higher than that of water ($
ho_{w} = 1\ g/cm^{3}$). A barometer measures atmospheric pressure by the height of the fluid column it can support. Using the formula $P =
ho gh$, for a given pressure $P$ (atmospheric pressure), a fluid with a higher density $
ho$ will have a shorter column height $h$. Water would require a column about 10.3 m high to measure standard atmospheric pressure, which is impractical, while mercury requires a column of about 760 mm.

Step7: Answer question 6

The maximum height to which a pump can lift water is limited by atmospheric pressure. A common pump works by creating a partial vacuum, and the atmospheric pressure then pushes the water up the pipe. The maximum height to which atmospheric pressure can push water is about 10.3 m (using $P=
ho gh$, where $P$ is atmospheric pressure, $
ho$ is the density of water, and $g$ is the acceleration due to gravity). The third - floor of an apartment complex is typically higher than 10.3 m, so a simple pump like the one shown cannot lift water to that height.

Step8: Answer question 7

One standard atmosphere of pressure (SP) is equivalent to 760 mmHg.

Answer:

1. Mercury is used due to its high density, resulting in a practical column - height for measuring atmospheric pressure.
2. The maximum height water can be lifted by atmospheric - pressure - based pumps is about 10.3 m, and the third - floor is usually higher than this.
3. 760
4. a. $\frac{320\times101.3}{760}\approx42.9$

b. $\frac{30.0\times760}{14.7}\approx1551$
c. $\frac{77.3\times760}{101.3}\approx579$