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Calculate the atmospheric pressure at sea level.

Physics

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Answer

217.6 m\textbf{217.6 m}

Step-by-step solution

4 steps
  1. Calculate the atmospheric pressure at sea level.

    The pressure (PP) due to a fluid column is given by the formula P=ρghP = \rho g h, where ρ\rho is the density of the fluid, gg is the acceleration due to gravity, and hh is the height of the fluid column.

    Given:
    Barometric height at sea level (hseah_{sea}) = 76 cm=0.76 m76 \text{ cm} = 0.76 \text{ m}
    Density of mercury (ρHg\rho_{Hg}) = 13600 kg/m313600 \text{ kg/m}^3
    Acceleration due to gravity (gg) = 10 N/kg=10 m/s210 \text{ N/kg} = 10 \text{ m/s}^2

    Pressure at sea level (PseaP_{sea}):

    Psea=ρHgghseaP_{sea} = \rho_{Hg} g h_{sea} Psea=13600 kg/m3×10 m/s2×0.76 mP_{sea} = 13600 \text{ kg/m}^3 \times 10 \text{ m/s}^2 \times 0.76 \text{ m} Psea=103360 PaP_{sea} = 103360 \text{ Pa}
  2. Calculate the atmospheric pressure at the highland.

    Barometric height at the highland (hhighh_{high}) = 74 cm=0.74 m74 \text{ cm} = 0.74 \text{ m}

    Pressure at the highland (PhighP_{high}):

    Phigh=ρHgghhighP_{high} = \rho_{Hg} g h_{high} Phigh=13600 kg/m3×10 m/s2×0.74 mP_{high} = 13600 \text{ kg/m}^3 \times 10 \text{ m/s}^2 \times 0.74 \text{ m} Phigh=100640 PaP_{high} = 100640 \text{ Pa}
  3. Determine the pressure difference between sea level and the highland.

    The pressure difference (ΔP\Delta P) is the difference between the pressure at sea level and the pressure at the highland.

    ΔP=Psea−Phigh\Delta P = P_{sea} - P_{high} ΔP=103360 Pa−100640 Pa\Delta P = 103360 \text{ Pa} - 100640 \text{ Pa} ΔP=2720 Pa\Delta P = 2720 \text{ Pa}
  4. Calculate the altitude of the point.

    The pressure difference is caused by the column of air between sea level and the highland. This pressure difference can also be expressed as ΔP=ρairgH\Delta P = \rho_{air} g H, where ρair\rho_{air} is the density of air and HH is the altitude.

    Given:
    Density of air (ρair\rho_{air}) = 1.25 kg/m31.25 \text{ kg/m}^3

    Rearrange the formula to solve for HH:

    H=ΔPρairgH = \frac{\Delta P}{\rho_{air} g} H=2720 Pa1.25 kg/m3×10 m/s2H = \frac{2720 \text{ Pa}}{1.25 \text{ kg/m}^3 \times 10 \text{ m/s}^2} H=272012.5 mH = \frac{2720}{12.5} \text{ m} H=217.6 mH = 217.6 \text{ m}

    The altitude of the point is:

    217.6 m\textbf{217.6 m}
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