Which of the following statements is true?

A. The weight of a column of seawater 1 m\(^2\) in cross-section and 10 m high is about 2.00 × 10\(^5\) N.

B. The weight of a column of seawater 1 m\(^2\) in cross-section and 10 m high, plus the weight of a column of air with the same cross-section extending up to the top of the atmosphere, is about 2.00 × 10\(^5\) N.

C. The weight of 1 m\(^3\) of seawater at 10 m below the surface of the ocean is about 2.00 × 10\(^5\) N.

D. The density of seawater is about 2.00 × 10\(^5\) times the density of air at sea level.

“The weight of a column of seawater [tex]1 \mathrm{m}^{2}[/tex] in cross section and 10 m high + the weight of a column of air with the same cross-section elongating up to the top of the atmosphere is about [tex]2.00 \times 10^{5} \mathrm{N}[/tex]” is true from the above-given sentences.

Explanation:

It depends on if you are talking about gauge pressure or total pressure. The “weight of a column” of seawater [tex]1 \mathrm{m}^{2}[/tex] in “cross section” and 10 m high is about [tex]2.00 \times 10^{5} \mathrm{N}[/tex]. This is gauge pressure, which considers the surrounding air pressure, and only reads off pressure above “air pressure”. “The weight of a column of seawater [tex]1 \mathrm{m}^{2}[/tex] in cross section and 10 m high + the weight of a column of air with the same cross-section elongating up to the top of the atmosphere is about [tex]2.00 \times 10^{5} \mathrm{N}[/tex]”. The “total pressure”, which considers the “pressure” of the whole which is above a certain height.

qwpink qwpink · Answer 2 · 2023-10-08T09:38:33-04:00

Final answer:

The true statement is that the combined weight of a column of seawater 1 m2 in cross section and 10 m high, plus the weight of a column of air with the same cross section up to the top of the atmosphere, is about 2.00× 105 N.

Explanation:

Given the information on atmospheric pressure and the properties of seawater and air at sea level, we can assess the statements.

Firstly, atmospheric pressure at sea level averages 1.01 × 105 Pa (equivalent to 1 atm), indicating that a column of air above 1 m2 extending up to the top of the atmosphere weighs 1.01 × 105 N.

The only statement among the provided options that is true is: The weight of a column of seawater 1 m2 in cross section and 10 m high plus the weight of a column of air with the same cross section extending up to the top of the atmosphere is about 2.00× 105 N. This is because the weight of the 10-meter high column of seawater (assuming a density of approximately 1025 kg/m3 for seawater) is about 1.01× 105 N, which when combined with the weight of the column of air, totals to approximately 2.00× 105 N.