Respuesta :
Answer:
The answer to this is
The column of water in meters that can be supported by standard atmospheric pressure is 10.336 meters
Explanation:
To solve this we first list out the variables thus
Density of the water = 1.00 g/mL =1000 kg/m³
density of mercury = 13.6 g/mL = 13600 kg/m³
Standard atmospheric pressure = 760 mmHg or 101.325 kilopascals
Therefore from the equation for denstity we have
Density = mass/volume
Pressure = Force/Area and for a column of water, pressure = Density × gravity×height
Therefore where standard atmospheric pressure = 760 mmHg we have for Standard tmospheric pressure= 13600 kg/m³ × 9.81 m/s² × 0.76 m = 101396.16 Pa
This value of pressure should be supported by the column of water as follows
Pressure = 101396.16 Pa = kg/m³×9.81 m/s² ×h
∴ [tex]h = \frac{101396.16}{(1000)(9.81)}[/tex] = 10.336 meters
The column of water in meters that can be supported by standard atmospheric pressure is 10.336 meters
The height above the column of water that can be supported by standard atmospheric pressure is 10.3 m.
The given parameters;
- density of water, [tex]\rho _w[/tex] = 1.00 g/mL = 1,000 kg/m³
- density of mercury, [tex]\rho _{Hg}[/tex] = 13.6 g/mL = 13,600 kg/m³
- standard atmospheric pressure, P = 101325 Pa
The height above the column of water that can be supported by standard atmospheric pressure is calculated as follows;
[tex]\rho gh = P\\\\h = \frac{101325}{9.8 \times 1000} \\\\h = 10.3 \ m[/tex]
Thus, the height above the column of water that can be supported by standard atmospheric pressure is 10.3 m.
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