Question

1.5 cubic meters of pure water flows over a water fall, falling 28 m. if all of the water's potential energy is converted to kinetic energy at the bottom of the falls, which then heats the water, what is the temperature increase of the water?

Answer 1

The temperature increase of the water falling over a waterfall can be calculated using the principle of conservation of energy. By converting the potential energy of the water to kinetic energy and then thermal energy, the temperature of the water increases. In this case, the temperature increase is 0.0687 °C.

Step-by-step explanation:

To determine the temperature increase of the water falling over the waterfall, we can use the principle of conservation of energy. The potential energy of the water is converted to kinetic energy as it falls, and then this kinetic energy is converted to thermal energy, thus increasing the temperature of the water.

We can calculate the change in potential energy using the formula: potential energy = mass * gravity * height. In this case, the water has a mass of 1.5 cubic meters * 1000 kg/cubic meter = 1500 kg, and it falls a height of 28 m. So the potential energy change is: PE = 1500 kg * 9.8 m/s^2 * 28 m = 411,600 J.

Since all of the potential energy is converted to thermal energy and the water has a heat capacity of 4000 J/kg/°C, we can calculate the temperature increase using the formula: temperature increase = thermal energy / (mass * heat capacity). Here, the thermal energy is 411,600 J and the mass is 1500 kg, so the temperature increase is: ΔT = 411,600 J / (1500 kg * 4000 J/kg/°C) = 0.0687 °C.