Final answer:
To increase pressure by 1 atm in a lake of alcohol, a depth of approximately 13 meters is required due to the lower density of alcohol (789 kg/m³) compared to water.
Step-by-step explanation:
To determine how deep you must dive in a lake of alcohol to increase pressure by 1 atm, you need to consider the specific gravity of the liquid. The pressure change due to the weight of the liquid is described by the hydrostatic pressure formula, which is P = ρgh, where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height or depth of the fluid. Since alcohol is less dense than water, you would need to dive deeper in alcohol than in water to experience an increase in pressure of 1 atm.
In water, the depth required to increase pressure by 1 atm is approximately 10.3 meters, as the density of water is about 1000 kg/m³ and atmospheric pressure is approximately 101,325 Pa (which is equivalent to 1 atm). Now, because the density of alcohol (ethanol) is approximately 789 kg/m³, you would need to dive deeper than 10.3 meters to achieve the same pressure increase. To calculate the specific depth, you would use the same hydrostatic pressure formula, adjusting for the density of alcohol.
Considering atmospheric pressure and knowing that 1 atm = 101,325 Pa, you can solve h = 101325 / (ρg). For example, using the density of ethanol and g = 9.8 m/s²: the depth h ≈ 101325 / (789 kg/m³ * 9.8 m/s²) ≈ 13 meters. Therefore, you would need to dive approximately 13 meters in a lake of alcohol to increase pressure by 1 atm.