During a deep breath, our lungs expand about 2.0 L against an external pressure of 101.3 kPa. 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: \( w = -P_{\text{ext}} \Delta V \), where \( w \) is the work done, \( P_{\text{ext}} \) 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. Therefore, \( \Delta V = 2.0 \text{ L} \times 0.001 \text{ m}^3/\text{L} \).
3. Substitute the given values into the formula: \( w = -(101.3 \text{ kPa}) \times (\Delta V \text{ in m}^3) \).
4. Convert the pressure from kilopascals to pascals, knowing that 1 kPa = 1000 Pa, so \( 101.3 \text{ kPa} = 101300 \text{ Pa} \).
5. Calculate the work done using the values in the formula, keeping in mind that the work will be in joules (J) since 1 Pa = 1 N/m² and 1 J = 1 N·m.

Key Concepts

Work in Thermodynamics

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

Pressure-Volume Work

Pressure-volume work occurs when a gas expands or contracts against an external pressure. The work done by the gas during expansion is directly proportional to the pressure exerted and the change in volume. Understanding this relationship is crucial for calculating the work done during processes like breathing, where lung volume changes against atmospheric pressure.

Units of Measurement

In this context, work is measured in joules (J), which is the SI unit of energy. One joule is defined as the work done when a force of one newton displaces an object by one meter. It is important to ensure that all units are consistent when performing calculations, particularly when converting pressure from kilopascals to pascals or volume from liters to cubic meters.