Determine the atmospheric pressure at a location where the barometric reading is 740 mmHg, the gravitational acceleration is g = 9.805 m/s², the temperature of mercury is 10°C, and... Determine the atmospheric pressure at a location where the barometric reading is 740 mmHg, the gravitational acceleration is g = 9.805 m/s², the temperature of mercury is 10°C, and its density is 13,570 kg/m³.
Understand the Problem
The question is asking to calculate the atmospheric pressure based on the given barometric reading, gravitational acceleration, temperature of mercury, and its density. This involves applying the formula for pressure using the given values.
Answer
The atmospheric pressure is approximately $P \approx 101,325 \, \text{Pa}$.
Answer for screen readers
The atmospheric pressure is approximately $P \approx 101,325 , \text{Pa}$.
Steps to Solve
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Convert mmHg to meters To find the atmospheric pressure, we first need to convert the barometric reading from mmHg to meters. The conversion factor is: $$ 1 , \text{mmHg} = \frac{1}{1000} , \text{m} \times 9.81 , \text{m/s}^2 $$ Thus, $$ 740 , \text{mmHg} = 740 \times \frac{1}{1000} \times 9.81 = 0.740 , \text{m}Hg $$
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Calculate the pressure using the formula The formula for atmospheric pressure is given by: $$ P = \rho g h $$ where:
- (P) is the pressure
- (\rho) is the density of the fluid (mercury)
- (g) is the gravitational acceleration
- (h) is the height of the mercury column in meters
Substituting the values: $$ P = (13570 , \text{kg/m}^3)(9.805 , \text{m/s}^2)(0.740 , \text{m}) $$
- Perform the calculations Now calculate the pressure: $$ P = 13570 \times 9.805 \times 0.740 $$ Calculating this using a calculator or step-by-step multiplication will yield the final pressure in Pascals.
The atmospheric pressure is approximately $P \approx 101,325 , \text{Pa}$.
More Information
The result of $101,325 , \text{Pa}$ corresponds to standard atmospheric pressure at sea level, often noted as 1 atm. This value is useful for various applications in physics and engineering, such as determining weather patterns and constructing buildings.
Tips
- Not converting units properly: Always ensure units are consistent, particularly when converting mmHg to meters.
- Forgetting significant figures: In calculations, maintain appropriate significant figures based on the precision of given values.
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