A fixed quantity of gas undergoes the reversible changes illustrated in the p-V diagram in Fig.

step 1 Let us solve the first part of this problem. Work done in isobaric process. Isobaric means const

A fixed quantity of gas undergoes the reversible changes...

Key Concepts

Integration in Thermodynamics

The application of integration in thermodynamics involves summing infinitesimal contributions of work done (P dV) along a process path. This concept is essential for calculating the area under the curve in a p-V diagram, which represents the work performed during the expansion or compression of a gas. The integration approach provides a link between the geometry of the p-V diagram and the energy interactions in the system.

Pressure-Volume (p-V) Diagram

A p-V diagram is a graphical representation where pressure is plotted on the vertical axis and volume on the horizontal axis. It is a fundamental tool in thermodynamics for visualizing and analyzing the behavior of gases undergoing various processes. The area under a process curve in a p-V diagram directly relates to the work done by or on the system during that process.

Thermodynamic Work

In thermodynamics, work is defined as the energy transferred when a system undergoes a change in volume under the action of external pressure. Mathematically, for a reversible process, the work done by the gas is computed as the definite integral of pressure with respect to volume (W = ?P dV). This expression emphasizes that work is path-dependent and varies with the specific path taken by the process in the diagram.

Reversible Process

A reversible process is one that proceeds in such a way that the system remains in thermodynamic equilibrium at every stage. This idealization allows for the precise calculation of work and heat transfer since the process can be reversed by an infinitesimal change in conditions. In the context of a p-V diagram, reversible processes assure that the integration of pressure with respect to volume yields exact work values.

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