Every second at Niagara Falls, some 5000 m^3 of water falls...

Every second at Niagara Falls, some $5000 \mathrm{~m}^{3}$ of water falls a distance of $50.0 \mathrm{~m}$ (Fig. $\mathrm{P} 22.48)$. What is the increase in entropy per second due to the falling water? (Assume that the mass of the surroundings is so great that its temperature and that of the water stay nearly constant at $20.0{ }^{\circ} \mathrm{C}$. Suppose that a negligible amount of water evaporates.)

Key Concepts

Gravitational Potential Energy

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. It is defined by the equation E = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height from which the object is falling. This concept is crucial in this problem because the falling water loses gravitational potential energy, which is then converted into other forms of energy such as kinetic and eventually thermal energy.

Entropy

Entropy is a measure of the disorder or randomness within a system. It increases when energy is dispersed in less usable forms, especially during irreversible processes like friction and turbulence. The change in entropy for a system undergoing a heat transfer at a constant temperature is given by ?S = Q/T, where Q is the heat added and T is the temperature in Kelvin.

Energy Conversion and Dissipation

This concept involves the transformation of energy from one form to another—in this case, from gravitational potential energy into kinetic energy and then into thermal energy. When the energy is dissipated as heat, it increases the entropy of the surroundings. This energy transformation is fundamental to understanding how natural processes, like water falling, contribute to the overall entropy of a system.

Thermodynamic Temperature

Thermodynamic temperature is the absolute temperature measured in Kelvin, which is essential for calculations in thermodynamics. In processes involving entropy changes, particularly when using the formula ?S = Q/T, the temperature of the surroundings (which remains constant in this problem) is used to determine how much the entropy increases as energy is transferred.

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