Lung Volume at Increased Water Pressure: A Boyle's Law Calculation

According to Boyle's Law, The volume of a given mass of gas is inversely proportional to the pressure exerted on the gas.

Given that,

Initial lung volume(at the water surface), \(V_1 = 0.5 L\)

Initial water pressure (at the water surface), \(P_1 = 1 atm\)

Final water pressure (at twice its value), \(P_2 = 2 atm\)

Using Boyle's Law, we can determine the final lung volume \(V_2\). The formula is:

\(P_1 V_1 = P_2 V_2\)

Substituting the given values into the formula, we get:

\(1 atm * 0.5 L = 2 atm * V_2\)

Rearranging to solve for \(V_2\), we get:

\(V_2 = \frac{1atm* 0.5L}{2 atm}\)

\(V_2 = 0.25L\)

Therefore, the lung volume at a depth where the water pressure is twice its value at the water surface would be approximately \(0.25 L\).