A reaction inside a cylindrical container with a movable RAN piston causes the volume to change from 12.0 L to 18.0 L while the pressure outside the container remains constant at 0.975 atm. (The volume of a cylinder is V = pr2h, where h is the height; 1 L # atm = 101.325 J.) (a) What is the value in joules of the work w done during the reaction?

Verified step by step guidance

1. Identify the formula for work done by a gas when the volume changes at constant pressure: \( w = -P_{\text{ext}} \Delta V \), where \( P_{\text{ext}} \) is the external pressure and \( \Delta V \) is the change in volume.
2. Calculate the change in volume \( \Delta V \) by subtracting the initial volume from the final volume: \( \Delta V = V_{\text{final}} - V_{\text{initial}} = 18.0 \text{ L} - 12.0 \text{ L} \).
3. Substitute the values of \( P_{\text{ext}} = 0.975 \text{ atm} \) and \( \Delta V \) into the work formula: \( w = -0.975 \text{ atm} \times \Delta V \).
4. Convert the work from L \( \cdot \) atm to joules using the conversion factor \( 1 \text{ L} \cdot \text{ atm} = 101.325 \text{ J} \).
5. Multiply the result from the previous step by 101.325 to find the work done in joules.

Key Concepts

Work in Thermodynamics

In thermodynamics, work is defined as the energy transferred when a force is applied over a distance. For gas systems, work can be calculated using the formula w = -P_extΔV, where P_ext 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 against an external pressure.

Pressure-Volume Work

Pressure-volume work occurs when a gas expands or contracts in a container, changing its volume. The work done by or on the gas is directly related to the pressure exerted on the gas and the change in volume. In this scenario, the constant external pressure allows for a straightforward calculation of work as the volume changes from 12.0 L to 18.0 L.

Unit Conversion in Thermodynamics

In thermodynamics, it is often necessary to convert units to ensure consistency in calculations. For example, work is commonly expressed in joules, and the relationship between liters and atmospheres to joules is given by 1 L·atm = 101.325 J. Understanding how to convert between these units is essential for accurately calculating work done in gas reactions.