Question

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

Answer 1

Answer:

The pressure at this depth is $1.235\cdot P_{atm}$.

Explanation:

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

$\frac{P_{2}}{P_{1}} = \frac{V_{1}}{V_{2}}$ (1)

Where:

$V_{1}, V_{2}$ - Initial and final volume.

$P_{1}, P_{2}$ - Initial and final pressure.

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

$\frac{P_{2}}{P_{1}} = 1.235$

If $P_{1} = P_{atm}$, then the final pressure of the gas is:

$P_{2} = 1.235\cdot P_{atm}$

The pressure at this depth is $1.235\cdot P_{atm}$.