In the accompanying cylinder diagram, a chemical process occurs at constant temperature and pressure. (a) Is the sign of w indicated by this change positive or negative?

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insert step 1> Identify the type of process occurring in the cylinder. Since the process occurs at constant temperature and pressure, it is likely an isothermal process.

insert step 2> Recall that work (w) in thermodynamics is related to the expansion or compression of gases. In an isothermal process, work is done by or on the system.

insert step 3> Determine the direction of the process. If the gas expands, it does work on the surroundings, and if it is compressed, work is done on the gas.

insert step 4> Use the sign convention for work: If the system does work on the surroundings (expansion), w is negative. If work is done on the system (compression), w is positive.

insert step 5> Based on the direction of the process (expansion or compression), determine the sign of w.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Work (w) in Thermodynamics

In thermodynamics, work (w) refers to the energy transferred when a force is applied over a distance. The sign of work is determined by the direction of energy transfer: positive work indicates that the system is doing work on the surroundings, while negative work means that work is done on the system by the surroundings.

Constant Temperature and Pressure

A process occurring at constant temperature and pressure is known as an isothermal and isobaric process, respectively. In such conditions, the system's internal energy remains constant, and any energy change is associated with work done or heat exchanged, which influences the sign of work.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. It relates the change in internal energy of a system to the heat added to the system and the work done by the system, expressed as ΔU = Q - w. Understanding this relationship is crucial for determining the sign of work in a given process.

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