During a normal breath, our lungs expand about 0.50 L against an external pressure of 1.0 atm. How much work is involved in this process (in J)?

Verified step by step guidance

1. Identify the formula for work done by a gas during expansion: \( w = -P_{\text{ext}} \Delta V \), where \( w \) is work, \( P_{\text{ext}} \) is the external pressure, and \( \Delta V \) is the change in volume.
2. Convert the volume change from liters to cubic meters, since 1 L = 0.001 m³. Thus, \( \Delta V = 0.50 \text{ L} = 0.50 \times 0.001 \text{ m}^3 \).
3. Use the given external pressure \( P_{\text{ext}} = 1.0 \text{ atm} \). Convert this pressure to pascals (Pa) using the conversion factor: 1 atm = 101325 Pa.
4. Substitute the values into the work formula: \( w = - (101325 \text{ Pa}) \times (0.50 \times 0.001 \text{ m}^3) \).
5. Calculate the work \( w \) in joules (J), keeping in mind that the negative sign indicates work done by the system (lungs) on the surroundings.

Key Concepts

Work in Thermodynamics

In thermodynamics, work is defined as the energy transferred when a force is applied over a distance. For gases, work can be calculated using the formula W = -PΔV, where W is work, P is pressure, and ΔV is the change in volume. The negative sign indicates that work is done by the system when it expands against an external pressure.

Pressure-Volume Work

Pressure-volume work occurs when a gas expands or contracts in response to external pressure. In the context of breathing, when the lungs expand, they do work against the atmospheric pressure. The amount of work done can be quantified by the product of the external pressure and the change in lung volume during inhalation or exhalation.

Units of Work

Work is measured in joules (J) in the International System of Units (SI). One joule is defined as the work done when a force of one newton displaces an object by one meter. In the context of the given question, converting the volume change from liters to cubic meters is necessary to ensure that the units are consistent when calculating work.