An average human produces about \(10 \mathrm{MJ}\) of heat each day through metabolic activity. If a human body were an isolated system of mass \(80 \mathrm{~kg}\) with the heat capacity of water, what temperature rise would the body experience? Heat capacity of water \(=4.2 \mathrm{~J} / \mathrm{K}-\mathrm{g} .\) (a) \(29.76^{\circ} \mathrm{C}\) (b) \(2.976 \mathrm{~K}\) (c) \(2.976 \times 10^{4 \circ} \mathrm{C}\) (d) \(0.029^{\circ} \mathrm{C}\)

Metabolic heat production is the energy released as heat by biochemical reactions in the body, particularly during the process of metabolism. This heat is essential in maintaining a constant internal body temperature despite varying environmental conditions.

When you undergo any physical activity or even while at rest, your cells are performing metabolism, which consists of breaking down nutrients to create energy. This energy is not just for moving or thinking, but also for the countless cellular activities that keep you alive. However, not all of this energy is utilized for work; much of it is lost as heat. This heat must be properly managed or it can lead to an increase in body temperature. Humans, and other mammals, have specialized means of regulating this heat through mechanisms like sweating and altering blood flow to the skin.

In the given exercise, the average human metabolic heat production is about 10 MJ (megajoules) per day. Without efficient heat dispersal, this would lead to an increase in body temperature, demonstrating the importance of thermoregulation.

The specific heat capacity is a property of a material that indicates how much heat energy (in joules) is required to raise the temperature of one gram of the material by one degree Celsius (or Kelvin). The specific heat capacity of water, for example, is relatively high, meaning it takes a considerable amount of heat to raise its temperature.

This property is crucial in many biological processes, as organisms are mostly water-based. A high specific heat capacity of water allows for better temperature regulation within the body, preventing sudden changes in temperature, which could be detrimental to enzyme function and other biochemical reactions. In the context of the exercise, the heat capacity of the water is used to emulate the human body's heat capacity because our bodies are composed largely of water.

Calculating temperature change involves determining how much an object's temperature will increase or decrease when a certain amount of heat is added or removed. This calculation requires knowledge of the specific heat capacity of the substance and the mass of the object being heated.

In the exercise, we applied the formula for temperature change, which is the heat produced divided by the product of the mass and the specific heat capacity. By carrying out this computation, the temperature change for the average human body based on metabolic heat production was found to be 29.76 degrees Celsius, indicating how much the body temperature would increase over one day if there were no means of heat dissipation.

Thermodynamics plays a vital role in biochemistry, which deals with understanding the energy changes associated with biochemical reactions. The principles of thermodynamics help explain how organisms obtain and use energy, how energy is transformed within cells, and how it influences the larger biological systems.

In biochemistry, the body is often compared to a thermodynamic system. This comparison allows us to use concepts like specific heat capacity and metabolic heat production to analyze the thermal behaviors of living beings. The exercise highlights the application of thermodynamics by calculating the temperature change as a result of metabolic heat production using the concept of specific heat capacity, all rooted in the laws of thermodynamics that govern energy transformations in biochemical systems.

Understanding these concepts is key to appreciating how efficiently the human body operates and the intricate balance it maintains through the conversion and release of energy.