Your lungs hold 4.2 L of air at a pressure of 101.3 kPa. If you are holding your breath and dive into a pool to a depth of 5.0 m below the surface of the water, what is the volume of the air in your lungs assuming that the temperature remains the same?

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The pressure in the lungs is equal to the pressure of the water outside the lungs. The pressure of the water at a depth of 5.0 m is:$$P = ho g h = (1000 	ext{ kg/m}^3)(9.81 	ext{ m/s}^2)(5.0 	ext{ m}) = 49.05 	ext{ kPa}$$The volume of the air in the lungs is inversely proportional to the pressure, so:$$V_2 = V_1 \frac{P_1}{P_2} = (4.2 	ext{ L}) \frac{101.3 	ext{ kPa}}{49.05 	ext{ kPa}} = 2.8 	ext{ L}$$

Your Lungs Hold 4