The specific gravity of mercury is 13.6, When the barometric pressure is 720 mm of Hg, what is the atmospheric pressure in kPa? 106 kPa 100 kPa 96.1 kPa
The Correct Answer and Explanation is:
To find the atmospheric pressure in kPa, we first need to understand the relationship between the given quantities: specific gravity of mercury, barometric pressure, and the required atmospheric pressure.
Step 1: Understanding Specific Gravity
Specific gravity is the ratio of the density of a substance to the density of water. For mercury (Hg), the specific gravity is 13.6, which means mercury is 13.6 times denser than water.
Step 2: Calculating the Height of the Mercury Column
The barometric pressure is given as 720 mm of Hg. This height is the column of mercury in a barometer and is used to measure atmospheric pressure. The pressure exerted by a liquid column is given by the formula:P=ρghP = \rho g hP=ρgh
Where:
- PPP is the pressure (in Pascals or Pa),
- ρ\rhoρ is the density of the fluid (mercury in this case),
- ggg is the acceleration due to gravity,
- hhh is the height of the fluid column (720 mm of Hg).
The density of mercury (ρHg\rho_{\text{Hg}}ρHg) can be calculated using the specific gravity. The density of water is approximately 1000 kg/m31000 \, \text{kg/m}^31000kg/m3, so:ρHg=13.6×1000 kg/m3=13600 kg/m3\rho_{\text{Hg}} = 13.6 \times 1000 \, \text{kg/m}^3 = 13600 \, \text{kg/m}^3ρHg=13.6×1000kg/m3=13600kg/m3
Now, we convert the height of the mercury column to meters:h=720 mm=0.72 mh = 720 \, \text{mm} = 0.72 \, \text{m}h=720mm=0.72m
Step 3: Finding the Pressure in Pascals
Using the formula P=ρghP = \rho g hP=ρgh, where g=9.81 m/s2g = 9.81 \, \text{m/s}^2g=9.81m/s2:P=13600 kg/m3×9.81 m/s2×0.72 mP = 13600 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2 \times 0.72 \, \text{m}P=13600kg/m3×9.81m/s2×0.72mP=96,019.2 Pa≈96.02 kPaP = 96,019.2 \, \text{Pa} \approx 96.02 \, \text{kPa}P=96,019.2Pa≈96.02kPa
Step 4: Conclusion
The atmospheric pressure, based on a barometric reading of 720 mm of Hg, is approximately 96.1 kPa.
So, the correct answer is 96.1 kPa.
