Evaporation of sweat is the human body's cooling mechanism. At body temperature, it takes 2.4 MJ/kg to evaporate water. Marathon runners typically lose about 3 L of sweat each hour. How much energy gets lost to sweating during a 3 -hour marathon?

The phenomenon of sweating is closely tied to the body's mechanism to maintain an optimal temperature. When we exercise or find ourselves in warm environments, our bodies produce sweat to keep cool. Sweat on the surface of our skin absorbs heat energy from our bodies to evaporate, a process requiring substantial amounts of energy.

During a marathon, runners often experience considerable energy loss through sweating. To quantify this, imagine the body as a system that expends energy for various functions, where evaporation of sweat is a significant factor. It's given that 2.4 megajoules of energy (MJ) is needed to evaporate a kilogram (kg) of sweat. Over the course of a three-hour marathon, a runner may lose about 3 liters of sweat per hour, which is approximately equivalent to 3 kg per hour given that the density of water is about 1 kg per liter. Therefore, an astounding 21.6 MJ of energy is used for this cooling process over three hours, illustrating how sweating is a critical yet energy-intensive function of the human body.

Understanding the thermodynamics of bodily functions can be intriguing. The core principle of thermodynamics that applies here is the first law, which is concerned with the conservation of energy. Our bodies transfer energy from the food we consume into various forms, one of which is used for the evaporation of sweat.

During physical exertion, as in a marathon, the energy converted to kinetic energy for muscle movement also generates heat as a by-product. This excess heat needs to be dissipated to keep the body's temperature within safe limits. Sweat absorption of thermal energy and its subsequent phase change from liquid to vapor is a practical application of thermodynamics observed in our daily lives.

This process can be thought of as a heat engine where the body uses metabolic energy to perform work, and then heat is expelled through sweating as part of the 'exhaust'. Thermodynamically, sweating is an essential biological function to manage the internal thermal environment and maintain homeostasis.

Heat transfer in humans takes place through several mechanisms: conduction, convection, radiation, and evaporation. Among them, evaporation is a key method for temperature regulation. The heat necessary to transform sweat from a liquid to a gas is taken from the human body, which in turn cools it down.

When we sweat, our bodies utilize the heat from the skin's surface to convert the sweat into vapor—a process scientifically known as evaporative cooling. This process is much like how a wet towel placed on a hot surface begins to dry over time as it absorbs heat. Essential aspects to understand include the high heat of vaporization of water, acknowledging that water requires a significant amount of energy to evaporate, and the body's ability to efficiently use the heat from its own metabolic processes to facilitate this form of heat transfer.

This mechanism is also an example of passive heat transfer, as it doesn't require active energy consumption such as shivering or muscle contractions. Instead, it leverages the existing thermal energy resulting from basal metabolic activities and motor movements—showcasing the efficiency of the human body in maintaining its thermal balance.