Understanding Negative Work in Thermodynamics: When Volume Increases at Constant Pressure

Thermodynamics is a branch of physics that deals with the relationships between heat, work, and energy. In this context, the concept of 'work' is often discussed in the context of changes in volume, particularly for gases. When dealing with processes at constant pressure, the work done by or on a system can be mathematically expressed as:

Mathematical Expression of Work

Work done by the system (or on the system) can be formulated as:

W -P ΔV

W: Work done by or on the system P: Constant pressure ΔV: Change in volume (Vfinal - Vinitial)

Understanding the Sign Convention

Work Done by the System

When considering work done by the system, there are two main scenarios:

Expansion: If the system expands, the volume increases, leading to a positive change in volume (ΔV 0). According to the sign convention, work done by the system is considered negative. Therefore, when the volume increases, we have: W -P ΔV 0

Work Done on the System

Conversely, when the volume decreases (ΔV 0):

The surroundings do work on the system, which is considered positive.

Intuitive Explanation

Expansion

The process of expansion requires the gas to perform work against the external pressure, such as the walls of a container. This work is derived from the internal energy of the gas, leading to a decrease in the system's energy.

Energy Transfer

The negative sign in the work equation (W -P ΔV) indicates that energy is leaving the system as work is done on the surroundings. Therefore, the work is considered negative when the volume increases.

Summary

In summary, work is considered negative at constant pressure when the volume is increasing because the system is doing work on its surroundings, leading to a loss of internal energy.

Conventions in Thermodynamics

The convention in thermodynamics is to approach things from the perspective of the system. Therefore:

Work done on a system (compression) is considered positive. Work done by the system (expansion) is considered negative. Work of expansion by the system is thus negative because the volume increases (ΔV 0).

Energy Transfer in the First Law of Thermodynamics

This convention simplifies the First Law of Thermodynamics, which can be expressed as:

dU dq dw

The internal energy (U) of the gas is increased by adding heat (q) or doing work of compression (dw -PexdV), and decreased by removing heat (q) or allowing the gas to perform work of expansion (dw -PexdV 0).

By adhering to this sign convention, thermodynamic processes become more intuitive and straightforward to understand, making the application of these principles more accessible to students and professionals alike.