Consider 5.5 L of a gas at a pressure of 3.0 atm in a cylinder with a movable piston. The exte

step 1 this particular portion wants us to calculate work based on a particular pressure in volume chan

Consider 5.5 L of a gas at a pressure of 3.0 atm in a...

Consider $5.5 \mathrm{~L}$ of a gas at a pressure of $3.0 \mathrm{~atm}$ in a cylinder with a movable piston. The external pressure is changed so that the volume changes to $10.5 \mathrm{~L}$. a. Calculate the work done, and indicate the correct sign. b. Use the preceding data but consider the process to occur in two steps. At the end of the first step, the volume is $7.0 \mathrm{~L}$. The second step results in a final volume of $10.5$ L. Calculate the work done, and indicate the correct sign. c. Calculate the work done if after the first step the volume is $8.0 \mathrm{~L}$ and the second step leads to a volume of $10.5 \mathrm{~L}$. Does the work differ from that in part b? Explain.

Consider $5.5 \mathrm{~L}$ of a gas at a pressure of $3.0 \mathrm{~atm}$ in a cylinder with a movable piston. The external pressure is changed so that the volume changes to $10.5 \mathrm{~L}$.
a. Calculate the work done, and indicate the correct sign.
b. Use the preceding data but consider the process to occur in two steps. At the end of the first step, the volume is $7.0 \mathrm{~L}$. The second step results in a final volume of $10.5$ L. Calculate the work done, and indicate the correct sign.
c. Calculate the work done if after the first step the volume is $8.0 \mathrm{~L}$ and the second step leads to a volume of $10.5 \mathrm{~L}$. Does the work differ from that in part b? Explain.

Key Concepts

Work in Thermodynamics

Work in thermodynamics refers to the energy transferred when a force is applied over a distance. In processes involving gases, work is typically calculated as the integral of pressure with respect to a change in volume. This concept is pivotal because it quantifies the energy exchanged between a system (such as a gas) and its surroundings during expansion or compression processes.

Sign Conventions for Work

The sign of work is crucial in thermodynamic calculations: work done by the system (for example, during expansion) is often considered negative because the system expends energy, while work done on the system (compression) is positive as energy is added to the system. This convention helps in consistently evaluating energy changes in various processes.

Path Dependence in Thermodynamic Processes

Unlike state functions, work is path-dependent, meaning that the work done during a process depends not only on the initial and final states but also on the specific path taken between these states. When a process is carried out in multiple steps, the total work is calculated as the sum of the work done in each individual step, which is a key concept in understanding thermodynamic processes.

Integration of Pressure over Volume Changes

Calculating the work done by a gas during expansion or compression involves integrating the pressure over the change in volume. For processes where pressure is constant, this simplifies to the product of the constant pressure and the change in volume. However, if pressure varies during the process, it must be integrated to account for the varying force applied at each infinitesimal change in volume.

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