The maximum pressure most organisms can survive is about 1000 times atmospheric pressure. Only small, simple organisms such as tadpoles and bacteria can survive such high pressures. What then is the maximum depth at which these organisms can live under the sea (assuming that the density of seawater is 1025 kg/m^3)?
To determine the maximum depth at which organisms can live under the sea, we need to understand the relationship between pressure and depth in a fluid medium.
The pressure in a fluid increases with depth due to the weight of the fluid above it. This relationship is described by Pascal's Law, which states that the pressure at any given point in a fluid is equal in all directions.
We can use the concept of pressure as a function of depth to calculate the maximum depth at which organisms can survive under the sea.
Given that the maximum pressure organisms can survive is about 1000 times atmospheric pressure, we need to convert atmospheric pressure to a unit that is commonly used in scientific calculations. One commonly used unit is pascals (Pa), where 1 atmosphere (atm) is approximately equal to 101,325 Pa.
So, the maximum pressure organisms can survive is 1000 times atmospheric pressure, which would be 1000 atmospheres or 1000 * 101,325 Pa = 101,325,000 Pa.
Next, we need to determine the pressure at a given depth under the sea. The pressure due to the weight of a fluid can be calculated using the equation:
Pressure = Density * Gravity * Depth
Where:
Density is the density of the fluid (1025 kg/m^3 for seawater)
Gravity is the acceleration due to gravity (approximately 9.8 m/s^2)
Now, we can rearrange the equation to solve for the depth:
Depth = Pressure / (Density * Gravity)
Substituting the values we have:
Depth = 101,325,000 Pa / (1025 kg/m^3 * 9.8 m/s^2)
Calculating this expression gives us the maximum depth at which organisms can survive under the sea.
P(water) = P0 + d*g*h
where P is the pressure of water, P0 is the atmospheric pressure of the air at the surface of the water, d is the density of water, g is the constant acceleration due to gravity, and h is the depth of the water beneath the surface
1000*P0 = P0 + 1025*9.8 * h
look up P0, and solve for h in the appropriate units