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To determine the pressure in a fluid at a given depth with the air-filled cartesian diver, we can employ Boyle's law, which states that the pressure in an ideal gas (held at constant temperature) is inversely proportional to its volume. At a fluid's surface, the pressure of the fluid is the same as the pressure of the atmosphere just above it, which we'll denote as LaTeX: P_{atm}P a t m. If the volume of air, which can be treated as an ideal gas here, in the cartesian diver decreases by 19% as it is lowered to a specific depth in the fluid, the pressure of the fluid at this depth, in terms of atmospheric pressure, is

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Answer:

The pressure at this depth is [tex]1.235\cdot P_{atm}[/tex].

Explanation:

According to the statement, the uncompressed fluid stands at atmospheric pressure. By Boyle's Law we have the following expression:

[tex]\frac{P_{2}}{P_{1}} = \frac{V_{1}}{V_{2}}[/tex] (1)

Where:

[tex]V_{1}, V_{2}[/tex] - Initial and final volume.

[tex]P_{1}, P_{2}[/tex] - Initial and final pressure.

If we know that [tex]V_{2} = 0.81\cdot V_{1}[/tex], then the pressure ratio is:

[tex]\frac{P_{2}}{P_{1}} = 1.235[/tex]

If [tex]P_{1} = P_{atm}[/tex], then the final pressure of the gas is:

[tex]P_{2} = 1.235\cdot P_{atm}[/tex]

The pressure at this depth is [tex]1.235\cdot P_{atm}[/tex].

Cricetus

The pressure of the fluid at this depth will be "1.16 [tex]P_{atm}[/tex]".

Pressure and Volume

According to the question,

Let,

The volume of surface be "100 units".

then,

The volume of depth be:

= 100 - 14

= 86 units

We know the relation,

P ∝ [tex]\frac{1}{V}[/tex]

here, PV = Constant

By using Boyle's law,

→ P₁ V₁ = P₂ V₂

or,

→     P₂ = [tex]\frac{P_1 V_1}{V_2}[/tex]

By substituting the values, we get

           = [tex]\frac{P_{atm}\times 100}{86}[/tex]

           = 1.16 [tex]P_{atm}[/tex]

Thus the above answer is appropriate.

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