The gas pressure is about 9.40 × 10⁴ Pa
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Further explanation
Let's recall Hydrostatic Pressure formula as follows:
[tex]\boxed{ P = \rho g h}[/tex]
where:
P = hydrosatic pressure ( Pa )
ρ = density of fluid ( kg/m³ )
g = gravitational acceleration ( m/s² )
h = height of a column of liquid ( m )
Let us now tackle the problem!
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Complete Question:
A U-shaped tube is connected to a box at one end and open to the air at the other end. The box is full of gas at pressure pgas, and the tube is filled with mercury of density 1.36 × 10⁴ kg/m³ . When the liquid in the tube reaches static equilibrium, the mercury column is h₁ = 10.5 cm high in the left arm and h₂ = 5.00 cm high in the right arm. Assume p_atmos = 1.00 atm , what is the gas pressure p_gas?
Given:
density of mercury = ρ = 1.36 × 10⁴ kg/m³
atmospheric pressure = p_o = 1.00 atm = 76 cmHg
height difference of liquid column = Δh = 10.5 - 5.00 = 5.5 cm
Asked:
gas pressure = p_gas = ?
Solution:
Because the height difference of mercury column is 5.5 cm , then the pressure difference between the left arm and the right arm will be 5.5 cmHg.
[tex]\Delta p = p_o - p_{gas}[/tex]
[tex]5.5 \texttt{ cmHg} = 76 \texttt{ cmHg} - p_{gas}[/tex]
[tex]p_{gas} = 76 \texttt{ cmHg} - 5.5 \texttt{ cmHg}[/tex]
[tex]p_{gas} = 70.5 \texttt{ cmHg}[/tex]
[tex]p_{gas} = 1.36 \times 10^4 \times 9.8 \times 0.705 \texttt{ Pa}[/tex]
[tex]p_{gas} = 93962.4 \texttt{ Pa}[/tex]
[tex]p_{gas} \approx 9.40 \times 10^4 \texttt{ Pa}[/tex]
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Learn more
- Buoyant Force : https://brainly.com/question/13922022
- Kinetic Energy : https://brainly.com/question/692781
- Volume of Gas : https://brainly.com/question/12893622
- Impulse : https://brainly.com/question/12855855
- Gravity : https://brainly.com/question/1724648
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Answer details
Grade: High School
Subject: Physics
Chapter: Pressure
