Atmospheric pressure on a distant planet causes water to rise to a height of 10 m inside an evacuated tube with its open end immersed in a container of water open to ambient pressure. What is the atmospheric pressure? (Note: The density of water is 10³ kg/m³ and the gravitational acceleration is 20 m/s²)

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Quizplus · Accepted Answer

11ecba2d_130c_98b0_a3bf_538ac654f9f6_MD0008_00 Pressure (P) is a force exerted perpendicular to an area. Atmospheric pressure (P_atm) refers to the pressure that gas molecules in the atmosphere exert on all terrestrial objects (eg, bodies of water, living beings). A simple fluid barometer is a device that may be used to measure P_atm. Unlike gases in the atmosphere, fluids occupying the evacuated tube of a simple fluid barometer are considered ideal and therefore do not expand or contract in response to local conditions such as weather and elevation. As a result, the hydrostatic pressure (P_h) generated by the fluid column inside of the barometer is a reliable estimate of local P_atm: 11ecba2d_130c_bfc1_a3bf_43ba051aa672_MD0008_00 P_h itself is related to the fluid density (ρ_f), gravitational acceleration (g), and total fluid column height (h). Therefore, P_atm may be quantified in terms of the variables influencing P_h: 11ecba2d_130c_bfc2_a3bf_e130f516fb18_MD0008_00 In this question, the P_atm of the distant planet (g = 20 m/s²) causes a column of water (ρ = 10³ kg/m³) to rise to a height of 10 m in an evacuated tube. Applying these values to the equation above yields P_atm: 11ecba2d_130c_bfc3_a3bf_53d71f2230d8_MD0008_00 11ecba2d_130c_bfc4_a3bf_4d998ac4c88c_MD0008_00 Reorganizing the units verifies that pascals (Pa), a common unit of pressure, are obtained: 11ecba2d_130c_bfc5_a3bf_6398580d8af1_MD0008_00 Therefore, it can be concluded that the P_atm of the distant planet is 2 × 10⁵ N/m² (Choice B), which is equivalent to 2 × 10⁵ Pa (1 N/m² = 1 Pa). Educational objective: A simple fluid barometer may be used to measure atmospheric pressure, the pressure exerted on all terrestrial objects by gas molecules in the atmosphere. Atmospheric pressure is equal to the hydrostatic pressure fluid column of a simple fluid barometer.

Atmospheric Pressure on a Distant Planet Causes Water to Rise