The waterfall "Angel Falls" in Venezuela is the world's tallest at h=979 m. Assume that the water's velocity on the top of the falls and on the bottom of the falls (after it hits the ground and begins to flow away) is equal, and that no total energy is lost by the water to the air/ground. Estimate the change in temperature of the water between the top and the bottom of the waterfall in Celsius.
To estimate the change in temperature of the water between the top and bottom of the waterfall, we can use the concept of potential energy and convert it to temperature change.
Here's how we can approach the problem:
1. Identify the potential energy change:
The potential energy of an object is given by the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
In this case, the potential energy change is equal to the change in height of the waterfall, which is h = 979 m.
2. Convert potential energy change to temperature change:
To convert the potential energy change to temperature change, we need to determine the specific heat capacity of water and the mass of the water.
The specific heat capacity of water, c, is approximately 4.18 J/g⋅°C.
We can assume a mass, m, of 1 gram for simplicity.
Now, we can calculate the change in temperature, ΔT, using the equation:
PE = mcΔT
Simplifying the equation, we have:
mgh = mcΔT
Canceling the mass and rearranging the equation, we get:
ΔT = gh/c
Substituting the given values:
ΔT = (9.8 m/s^2)(979 m) / (4.18 J/g⋅°C)
Calculating the result:
ΔT ≈ 234 °C
So, the estimated change in temperature of the water between the top and bottom of the Angel Falls in Venezuela is approximately 234 degrees Celsius.