At room temperature (25oC) and normal atmospheric pressure (760 torr), the average person’s lungs have a total capacity of about 5.5 liters. If a person takes a deep breath and then dives deep into a lake where the temperature is 19oC and a pressure of 915 torr, what will be the new volume of air in his lungs?
(P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.
To determine the new volume of air in the person's lungs, we can use the combined gas law formula, which relates the initial and final conditions of temperature, pressure, and volume of a gas.
The combined gas law formula is given by:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure (760 torr)
V1 = initial volume (5.5 liters)
T1 = initial temperature (25°C or 298K)
P2 = final pressure (915 torr)
V2 = final volume (unknown)
T2 = final temperature (19°C or 292K)
Rearranging the formula to solve for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
Substituting the given values:
V2 = (760 torr * 5.5 liters * 292K) / (915 torr * 298K)
Calculating this expression:
V2 ≈ 11.2 liters
Therefore, the new volume of air in the person's lungs after diving into the lake will be approximately 11.2 liters.