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When air is inhaled, it quickly becomes saturated with water vapor as it passes through the moist upper airways. When a person breathes dry air, about 25 mg of water are exhaled with each breath. At 12 breaths/min, what is the rate of energy loss due to evaporation? Express your answer in both watts and Calories per day. At body temperature, the heat of vaporization of water is \(L_{\mathrm{v}}=24 \times 10^{5} \mathrm{J} / \mathrm{kg}\).

Short Answer

Expert verified
The rate of energy loss due to evaporation is \(x\) Watts. The daily energy loss due to evaporation is \(y\) Calories.

Step by step solution

01

Calculate the total mass of water exhaled per minute

The total mass of water exhaled per minute can be calculated by multiplying the mass of water exhaled per breath \(25 mg\) by the breathing rate \(12 breaths/min\). Use the unit conversion \(1 g = 10^3 mg\) and \(1 kg = 10^3 g\) to convert the mass from milligrams to kilograms.
02

Calculate the total energy loss per minute

The total energy loss due to evaporation of water per minute can then be calculated using the formula for heat loss:\[ Q = m \cdot L_v \]where \(m\) is the mass of water exhaled per minute and \(L_v\) is the heat of vaporization of water. Substitute the calculated mass and the given \(L_v\) value into this equation to calculate the energy loss per minute, in Joules.
03

Convert energy loss to power

To convert the energy loss to power (energy rate), divide the energy loss per minute by the number of seconds in a minute (60), because power is measured in Joules per second or watts.
04

Convert power to daily energy loss in Calories

To express the daily energy loss in Calories, first convert the energy loss per second to energy loss per day by multiplying by the number of seconds in a day (86400). Then, convert the energy loss from Joules to Calories using the conversion factor \(1 Calorie = 4.184 \times 10^3 Joules\).

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Key Concepts

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

Heat of Vaporization
Understanding the heat of vaporization is crucial when examining the energy loss during processes like evaporation, boiling, or condensation. It's defined as the amount of energy needed to convert a given mass of a substance from a liquid into a gas at constant temperature and pressure.

In the context of respiratory physiology, it pertains to the energy the body must expend to convert the water in the respiratory tract from liquid to vapor during exhalation. For water, this value can be quite high, as water has a relatively strong intermolecular force holding its molecules together. The heat of vaporization for water at body temperature is given as 2,440 kJ/kg.

In our exercise, we use the heat of vaporization of water to calculate the total energy loss due to evaporation in the respiratory process. By understanding this concept and its numeric value, students can apply it to various problems involving phase changes from liquid to gas and vice versa.

Moreover, the heat of vaporization can vary depending on the temperature. It's important to use the value appropriate for the temperature of the substance. In the case of the human body, using the heat of vaporization at body temperature is necessary for an accurate calculation of energy loss during exhalation.
Energy Conversion in Physics
In the realm of physics, energy conversion signifies the process of changing one form of energy into another. Energy can be neither created nor destroyed, but it can transform from kinetic to potential energy, from chemical energy to thermal energy, and so on. This principle is known as the conservation of energy, and it is a fundamental concept in physics.

When discussing the energy loss due to evaporation in our exercise, we're essentially looking at the conversion of internal energy, in the form of heat, into the kinetic energy of water molecules which allows them to transition from a liquid to a gaseous state. This process entails the water vapor carrying away energy from the body, resulting in a loss of thermal energy or heat.

By applying the given heat of vaporization, and calculating the mass of water exhaled, students can quantify this energy conversion. Energy loss, measured in joules (J), is sometimes more practically expressed in terms of power, in watts (W), which represents the rate of energy conversion, and in Calories, which is common in biological and nutritional contexts.
Respiratory Physiology
Delving into respiratory physiology allows us to appreciate how energy loss due to evaporation plays a role in the human body. The respiratory system is not only responsible for gas exchange but also regulates the temperature and moisture level of the air entering our lungs.

When we inhale, the air is humidified and heated to body temperature by the upper respiratory tract, which consumes energy. As we exhale, this moist, warm air loses water vapor to the environment, which translates to energy loss from the body, particularly through the heat of vaporization. This loss is a necessary physiological process that maintains homeostasis but also represents a significant energy expenditure over time.

For a typical adult at rest, the rate of breathing is about 12 breaths per minute. Considering that each breath involves the evaporation of water, and applying the concept of heat of vaporization, students can calculate the rate of energy loss, anchoring theoretical physics in the tangible reality of human biology. It's essential for students to realize that this physiological process is a continuous and automatic adjustment governed by complex feedback systems in our bodies, crucial for survival.

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Most popular questions from this chapter

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