To determine the difference in temperature between the top and bottom of the waterfall, we need to consider the conversion of potential energy to heat energy.
The potential energy of an object is given by the formula:
Potential Energy = mass * gravity * height
In this case, the potential energy of the water at the top of the waterfall is converted into heat energy. Given that 75% of the potential energy is converted into heat, we can calculate the heat energy released:
Heat Energy = 0.75 * Potential Energy
Since the mass of the water cancels out in the calculation, we can focus on the height difference. The height difference between the top and bottom of the waterfall is 120 meters. So, the heat energy released can be expressed as:
Heat Energy = 0.75 * (mass * gravity * height)
Now, we can relate the heat energy released to the temperature difference using the equation:
Heat Energy = mass * specific heat capacity * temperature difference
The specific heat capacity of water is approximately 4.186 J/g°C. Assuming the mass of the water remains constant, we can rearrange the equation to solve for the temperature difference:
Temperature difference = Heat Energy / (mass * specific heat capacity)
Since the mass of the water is not provided, we cannot calculate the exact temperature difference without this information. However, you can use this formula with the given mass of the water to determine the temperature difference.
Please note that this calculation assumes there are no other energy losses or gains during the conversion process. In reality, factors such as air resistance and evaporation could affect the final temperature difference.