Problem 37 - University Physics with Modern Physics

Question

Digesting fat produces 9.3 food calories per gram of fat, and typically 80% of this energy goes to heat when metabolized. (One food calorie is 1000 calories and therefore equals 4186 J.) The body then moves all this heat to the surface by a combination of thermal conductivity and motion of the blood. The internal temperature of the body (where digestion occurs) is normally 37\(^\circ\)C, and the surface is usually about 30\(^\circ\)C. By how much do the digestion and metabolism of a 2.50-g pat of butter change your body's entropy? Does it increase or decrease?

Step-by-Step Solution

Answer

Entropy increases as heat is transferred from the internal body to the surface.

Step 1: Calculate the energy produced from fat

First, find out how much energy is produced by digesting 2.50 grams of fat. Given: - Each gram of fat produces 9.3 food calories.- 1 food calorie = 4186 J.Energy produced (in J) = \( 2.50 \times 9.3 \times 4186 \). Calculate this to find the total energy produced.

Step 2: Determine energy used as heat

From the total energy produced, 80% goes to heat.Energy as heat (in J) = \( 0.80 \times \text{Energy produced} \). Calculate this to find the energy being dissipated as heat.

Step 3: Calculate the change in entropy

The change in entropy \( \Delta S \) associated with moving the heat to the body's surface can be calculated using:\[ \Delta S = \frac{Q}{T} \]where:- \( Q \) is the energy as heat (from Step 2),- \( T \) is the average temperature in Kelvin.Convert temperatures from Celsius to Kelvin (K = °C + 273):- Internal temperature = 310 K- Surface temperature = 303 K\( \Delta S = \frac{Q}{T_{surface}} - \frac{Q}{T_{internal}} \)Substitute the values and solve to find the change in entropy.

Step 4: Analyze the change in entropy

Since the heat is being transferred from a warmer to a cooler area (from 37°C to 30°C or 310 K to 303 K), the entropy change will indicate whether entropy increases or decreases, which usually increases as heat is dissipated to the surrounding environment.

Key Concepts

Energy Metabolism

Energy metabolism is a crucial biological process where the body converts the food we consume into energy. This process involves breaking down nutrients like fats into usable energy forms for the body. When it comes to fat digestion, each gram of fat releases a significant amount of energy—about 9.3 food calories. This energy release is vital for powering the body's activities.

During energy metabolism, not all energy is directly usable for physical activities. A large portion of it, typically 80%, is dissipated as heat. This heat is essential for maintaining body temperature and supporting metabolic activities. Understanding how energy is metabolized helps in recognizing how the body functions efficiently, even during rest or digestion.

Efficient energy metabolism is integral for overall health as it affects how well the body can perform everything from cellular processes to physical activities. By studying energy metabolism, we can gain insights into dietary requirements and metabolic health.

Thermodynamics

Thermodynamics is the study of energy transformations, particularly how heat is utilized and transferred within systems. It plays a significant role in understanding how our bodies manage energy and maintain homeostasis through processes like fat digestion. A key principle of thermodynamics is the concept of energy conservation and entropy, which refers to the measure of disorder or randomness in a system.

In biological systems, such as the human body, thermodynamics explains how energy is transferred and transformed. During fat digestion, the body's internal temperature is maintained at around 37°C, and this energy needs to be efficiently managed to support metabolic processes. Thermodynamics also elucidates how energy is partially converted into heat, which must then be transported across the body to regulate temperature.

Understanding thermodynamics in biological systems helps us appreciate the delicate balance our body maintains in energy distribution and temperature regulation. This insight is crucial for fields like nutrition, physiology, and even medical diagnostics.

Heat Transfer

Heat transfer in the human body is an ongoing process essential for temperature regulation. During fat digestion, heat is generated as a byproduct of metabolism, and efficient heat transfer is necessary to maintain optimal body functioning. The human body employs different mechanisms to transfer heat, such as thermal conduction and blood circulation.

Thermal conductivity involves direct heat transfer through tissues, while blood flow helps redistribute heat away from core organs to the skin's surface, where it can dissipate into the environment. This process is crucial, especially when the body needs to adapt to varying external temperatures.

Heat transfer models help us understand how various factors, such as metabolic rate and environmental conditions, influence the body's ability to regulate temperature. By studying heat transfer, we can also learn how to improve health outcomes, manage fevers, or aid recovery from physical exertion.

Fat Digestion

Fat digestion is a complex but vital process where dietary fats are broken down into fatty acids and glycerol, which the body uses for energy or stores for later use. This process begins in the small intestine, aided by enzymes and bile acids, and provides more calories per gram than proteins or carbohydrates. It is for this reason that fats are an important energy source for the body.

Each gram of fat yields about 9.3 food calories, making it a dense energy source. The digestion and metabolism of fats release not just energy but also involve the release of heat, which has various roles, including maintaining body temperature. The body uses only a portion of the energy for immediate needs, while the rest is stored as potential energy.

Understanding fat digestion is critical for nutrition science as it influences dietary guidelines and health recommendations. It also sheds light on metabolic disorders related to fat intake and obesity, making it a focal point for both prevention and treatment strategies.