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In very cold weather, a significant mechanism for heat loss by the human body is energy expended in warming the air taken into the lungs with each breath. (a) On a cold winter day when the temperature is \(-20^{\circ} \mathrm{C},\) what is the amount of heat needed to warm to internal body temperature \(\left(37^{\circ} \mathrm{C}\right)\) the \(0.50 \mathrm{~L}\) of air exchanged with each breath? Assume that the specific heat of air is \(1020 \mathrm{~J} /(\mathrm{kg} \cdot \mathrm{K})\) and that \(1.0 \mathrm{~L}\) of air has a mass of \(1.3 \mathrm{~g}\). (b) How much heat is lost per hour if the respiration rate is 20 breaths per minute?

Short Answer

Expert verified
37.923 J of heat is needed per breath, and 45508 J per hour is lost with 20 breaths/min.

Step by step solution

01

Find Mass of Air per Breath

Given that 1.0 L of air has a mass of 1.3 g, we need to find the mass of 0.50 L of air exchanged per breath. Calculate the mass of air for 0.50 L using the formula:\[\text{mass} = \text{volume} \times \text{density} = 0.50 \text{ L} \times \frac{1.3 \text{ g}}{1 \text{ L}} = 0.65 \text{ g}\] Convert this mass to kilograms:\[0.65 \text{ g} = 0.00065 \text{ kg} \]
02

Calculate Heat Required per Breath

To calculate the heat required to warm the air from \(-20^{\circ} \text{C}\) to \(37^{\circ} \text{C}\), use the formula:\[q = m \cdot c \cdot \Delta T\]where \(m = 0.00065 \text{ kg}\), \(c = 1020 \text{ J/kg} \cdot \text{K}\), and \(\Delta T = 37 + 20 = 57 \text{ K}\).Thus, \[q = 0.00065 \times 1020 \times 57 = 37.923 \text{ J}\]Therefore, 37.923 J of heat is required per breath.
03

Calculate Total Heat Loss Per Hour

Calculate the number of breaths per hour. Given the respiration rate is 20 breaths per minute:\[\text{breaths per hour} = 20 \text{ breaths/min} \times 60 \text{ min/hour} = 1200 \text{ breaths/hour}\]Now calculate the total heat loss per hour:\[\text{total heat loss} = 37.923 \text{ J/breath} \times 1200 \text{ breaths/hour} = 45508 \text{ J/hour}\]Therefore, the total heat loss per hour is 45508 J.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Specific Heat Capacity
Specific heat capacity is a fundamental concept in thermodynamics, crucial for understanding how different substances respond to heat changes. It is defined as the amount of heat required to change the temperature of one kilogram of a substance by one degree Celsius. This property can vary significantly between different materials. For instance, air has a specific heat capacity of 1020 J/(kg·K), as mentioned in the exercise.

When considering the process of warming air during respiration, the specific heat capacity of air helps us determine the energy (heat) required to raise the temperature of inhaled air from a cold environment (e.g., -20°C) to body temperature (37°C). Knowing how much air is breathed in each breath, and its mass, allows us to use the formula: \[ q = m \cdot c \cdot \Delta T \]In this equation, \( q \) represents the heat energy required, \( m \) is the mass of the air, \( c \) is the specific heat capacity, and \( \Delta T \) is the change in temperature.
  • Use the specific heat of air to calculate the energy needed for temperature adjustments.
  • Apply this in situations like heating air for breathing, especially in cold conditions.
Influence of Respiration Rate
Respiration rate is a biological parameter referring to how many breaths an organism takes per minute. It can fluctuate based on numerous factors, such as physical activity, ambient temperature, and even stress levels. In our exercise, we consider a constant respiration rate of 20 breaths per minute. This rate is critical because it directly influences the total amount of heat energy exchanged due to breathing.

Higher respiration rates mean the body exchanges more air, and consequently, more heat energy per unit of time is needed to warm this air. Using the given formula for heat per breath, multiplying it by the number of breaths per hour gives us an understanding of the total energy expenditure for temperature regulation via respiration. Calculations here show this mechanism's significance in total heat loss, particularly in cold environments.
Mechanism of Heat Transfer
Heat transfer within biological systems is an essential process for maintaining homeostasis—keeping the internal environment stable. In simple terms, heat transfer involves the movement of thermal energy from warmer to cooler areas. Within the context of the exercise, heat transfer is the body's process of warming inhaled air to the necessary temperature for metabolic efficiency.

There are several modes of heat transfer: conduction, convection, and radiation. For the process of warming inhaled air, convection predominantly occurs. Air in the lungs absorbs heat from the surrounding tissues, thus warming up to match body temperature.
  • Heat is transferred from blood and lung tissues to the colder inhaled air.
  • Efficient transfer ensures body functions are not disrupted by external temperatures.
Understanding these processes helps elucidate how organisms survive in different thermal environments.
Thermodynamics in Biological Systems
Biological systems operate on the fundamental principles of thermodynamics. These systems must constantly manage heat generation and dissipation to sustain life processes effectively. For instance, while exercising or simply existing in cold weather, organisms face significant challenges in heat regulation.

Energy derived from nutrients during metabolic processes must be distributed to maintain body temperature and process functions such as respiration. Heat produced needs to be carefully managed given the body's set temperature range. Processes like breathing, mentioned in our exercise, are integral to managing these thermal dynamics by adjusting intake air temperature to a survivable level.
  • Thermodynamics ensure energy used in biological processes is efficiently controlled.
  • Understanding this aids in grasping how organisms cope with diverse environments.
This thermodynamic balance is critical for efficient body function and energy conservation, vital for survival in varying external temperatures.

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Most popular questions from this chapter

Convert the following Kelvin temperatures to the Celsius and Fahrenheit scales: (a) the midday temperature at the surface of the moon \((400 \mathrm{~K}) ;\) (b) the temperature at the tops of the clouds in the atmosphere of Saturn \((95 \mathrm{~K}) ;\) (c) the temperature at the center of the sun \(\left(1.55 \times 10^{7} \mathrm{~K}\right)\)

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