Imagine a reaction that results in a change in both volume and temperature: (a) Has any work been done? If so, is its sign positive or negative?

Verified step by step guidance

1. 1. In the context of chemistry, work is done when a system expands or contracts against an external pressure. If the volume of the system changes, it means that work has been done.
2. 2. The sign of the work done depends on the direction of the volume change. If the system expands (volume increases), it does work on the surroundings, and the work is considered negative. This is because the system is losing energy to do the work. In contrast, if the system contracts (volume decreases), work is done on the system by the surroundings, and the work is considered positive because the system is gaining energy.
3. 3. The change in temperature does not directly indicate whether work has been done or not. However, it can be related to the change in internal energy of the system. If the temperature increases, the internal energy of the system increases and vice versa. But this change in internal energy can be due to work done on or by the system, heat transferred to or from the system, or both.
4. 4. To determine the exact amount of work done, you would need more information such as the external pressure and the exact change in volume. The work done (w) can be calculated using the formula w = -PΔV, where P is the external pressure and ΔV is the change in volume.
5. 5. Remember, these signs are based on the convention used in chemistry. In physics, the signs may be reversed. Always pay attention to the context and the convention being used.

Key Concepts

Work in Thermodynamics

In thermodynamics, work is defined as the energy transferred when a force is applied over a distance. For a gas, work can be calculated using the formula W = -PΔV, where P is pressure and ΔV is the change in volume. If the volume increases (expansion), work is done by the system and is considered negative, while if the volume decreases (compression), work is done on the system and is positive.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. This principle implies that the change in internal energy of a system (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W): ΔU = Q - W. Understanding this relationship is crucial for analyzing energy changes in reactions involving volume and temperature changes.

Sign Convention for Work

The sign convention for work in thermodynamics is essential for determining the direction of energy transfer. When a system does work on its surroundings (expansion), the work is considered negative, indicating energy leaving the system. Conversely, when work is done on the system (compression), it is positive, reflecting energy entering the system. This convention helps clarify the energy dynamics during reactions that involve changes in volume and temperature.