Question

According to Boyle's law, the product of pressure and volume is a constant. Hence, (a) if volume of lungs is increased, the pressure decreases proportionately (b) if volume of lungs is increased, the pressure also increases proportionately (c) if volume of lungs is increased, the pressure decreases disproportionately (d) if volume of lungs is increased, the pressure remains the same.

Short answer

If the volume of the lungs is increased, the pressure decreases proportionately according to Boyle's Law (option a).

Step-by-step solution

Understanding Boyle's Law

Boyle's Law states that for a given mass of an ideal gas at constant temperature, the product of pressure (P) and volume (V) is a constant (k). Mathematically, it can be expressed as P * V = k, where P is the pressure, V is the volume, and k is a constant value. When the volume increases, the pressure must decrease to maintain the constant product, provided the temperature and mass of the gas remains unchanged.

Analyzing the Effects of Increased Volume on Pressure

According to Boyle's Law, if the volume of the lungs is increased, the pressure of the gas inside must decrease in order to maintain a constant product. Therefore, when volume goes up, pressure goes down proportionately, assuming a closed system where the temperature and amount of gas do not change.

Eliminating Incorrect Options

Analyzing the effects per Boyle's Law, we can eliminate options (b), (c), and (d). Since they suggest that pressure increases, stays the same, or decreases disproportionately when volume is increased, which does not align with the law.

Key concepts

Pressure-Volume Relationship

One of the fundamental principles in physics and chemistry is the relationship between the pressure and volume of a gas, perfectly illustrated by Boyle's Law. This law tells us that for a given amount of an ideal gas kept at a constant temperature, when we increase the volume, the pressure decreases and vice versa. This inverse relationship is crucial for understanding how various systems, such as engines and respiratory systems, operate.

For instance, let's consider a syringe filled with air; if you pull the plunger back, you increase the volume inside the syringe. As per Boyle's Law, the pressure inside decreases, which is why the syringe can easily pull in fluids when the plunger is pulled back. Conversely, pushing the plunger in decreases the volume and increases the pressure, expelling the fluid. To depict this mathematically, the formula is written as \( P \times V = k \), where \( P \) is pressure, \( V \) is volume, and \( k \) remains a constant when the temperature is unchanged.

Applications in Real Life

Understanding this concept is not only vital for academic purposes but also for practical applications like operating a bicycle pump, using a spray can, or even in the medical field when assessing the functioning of the lungs.

Lung Volume Physiology

The physiology of the respiratory system is intricately linked with the principles of Boyle's Law. In fact, our lungs function by utilizing the pressure-volume relationship. As we inhale, the diaphragm and intercostal muscles contract, expanding the chest cavity and increasing the lung volume. This action leads to a decrease in pressure within the lungs compared to the outside atmosphere, causing air to rush in to equalize the pressure.

During exhalation, the process reverses; the diaphragm relaxes, the chest cavity’s volume decreases, and the pressure inside the lungs increases, prompting the air to flow out. This demonstrates how Boyle’s Law operates with each breath we take, maintaining the crucial balance of air movement that is essential for oxygen exchange and the removal of carbon dioxide from the body.

The Importance of Lung Volume in Health

Medical professionals often measure lung volume as an indicator of a person's respiratory health. Conditions such as asthma, emphysema, and chronic obstructive pulmonary disease (COPD) can alter the pressure-volume relationship in the lungs, leading to difficulties in breathing and adequate oxygenation of the blood.

Ideal Gas Law

While Boyle's Law is a particular instance of the behavior of gases, it's part of a broader concept known as the Ideal Gas Law. This law combines several gas laws, including Boyle’s, Charles’s, and Avogadro’s, into a single equation: \( PV = nRT \). In this equation, \( P \) stands for the pressure of the gas, \( V \) is the volume, \( n \) is the number of moles of gas, \( R \) is the gas constant, and \( T \) is the temperature in Kelvin.

This law provides a more comprehensive understanding as it accounts for changes in the amount of gas and temperature, factors that Boyle's Law holds constant. The Ideal Gas Law is pivotal in fields like meteorology, engineering, and even in everyday cooking where the behavior of gases under different conditions is an important consideration. It explains why a sealed bag of chips may burst when taken to higher altitudes or why car tires need to be inflated or deflated when temperatures change drastically.

Connecting to Real-World Scenarios

By understanding the Ideal Gas Law, individuals can better comprehend how changes in one variable affect the others, which is beneficial not only academically but also in their daily lives. For instance, knowing to adjust tire pressure according to weather extremes is a practical application of this law.