If the loss in gravitational potential energy of a volume of water falling 100 meters (quite a high waterfall!) were converted completely to heat, the resultant rise in temperature of the water would be on the order of

Question

Quizplus · Accepted Answer

The loss in gravitational potential energy (GPE) when converted to heat energy can be calculated using the formula for GPE, which is $mgh$, where $m$ is the mass of the object (in this case, water), $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), and $h$ is the height from which the object falls. The energy converted to heat would then cause the water to warm up. The specific heat capacity of water is approximately $4,200 \, \text{J/kg}^\circ\text{C}$, meaning it takes 4,200 Joules to raise 1 kilogram of water by 1 degree Celsius. Given these values, a 100-meter fall would result in a temperature increase on the order of 1 degree Celsius, assuming 100% conversion of potential energy to heat and no loss of energy to the surroundings.

If the Loss in Gravitational Potential Energy of a Volume