The water flowing over Niagara Falls drops a distance of 50 m.If all the gravitational potential energy of the system water-Earth is converted to thermal energy,by what temperature does the water rise? The specific heat of water is 4186 J/kg ∙ K.

Question

Quizplus · Accepted Answer

The temperature rise can be calculated using the formula for gravitational potential energy (GPE) converted to thermal energy: $\Delta T = \frac{GPE}{m \cdot c}$, where $GPE = m \cdot g \cdot h$, $m$ is the mass of the water (which will cancel out), $g$ is the acceleration due to gravity (9.8 m/s$^2$), $h$ is the height (50 m), and $c$ is the specific heat capacity of water (4186 J/kg·K). Plugging in the values: $\Delta T = \frac{9.8 \cdot 50}{4186} = 0.117$ C°, which rounds to 0.12 C°.

The Water Flowing Over Niagara Falls Drops a Distance of 50