(a) Write an equation that expresses the first law of thermodynamics in terms of heat and work. (b) Under what conditions will the quantities q and w be negative numbers?

Verified step by step guidance

Step 1: Recall the first law of thermodynamics, which states that the change in internal energy of a system (\( \Delta U \)) is equal to the heat added to the system (\( q \)) plus the work done on the system (\( w \)). This can be expressed as the equation: \( \Delta U = q + w \).

Step 2: Understand that in thermodynamics, the sign conventions for heat (\( q \)) and work (\( w \)) are important. Heat added to the system is positive, and heat released by the system is negative. Similarly, work done on the system is positive, and work done by the system is negative.

Step 3: Consider the conditions under which \( q \) would be negative. This occurs when the system releases heat to the surroundings, such as in an exothermic reaction.

Step 4: Consider the conditions under which \( w \) would be negative. This happens when the system does work on the surroundings, such as when a gas expands against an external pressure.

Step 5: Summarize that both \( q \) and \( w \) are negative when the system is losing energy to the surroundings, either by releasing heat or by doing work on the surroundings.

Key Concepts

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

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. It can be expressed mathematically as ΔU = q + w, where ΔU is the change in internal energy, q is the heat added to the system, and w is the work done on the system. This principle underpins the conservation of energy in thermodynamic processes.

Heat (q)

In thermodynamics, heat (q) refers to the energy transferred between a system and its surroundings due to a temperature difference. When heat is absorbed by the system, q is positive, while if heat is released to the surroundings, q is negative. Understanding the sign convention for heat is crucial for analyzing energy changes in thermodynamic processes.

Work (w)

Work (w) in thermodynamics is defined as the energy transferred when a force is applied over a distance. In the context of a system, work is considered positive when done on the system (compression) and negative when done by the system (expansion). Recognizing the conditions under which work is positive or negative is essential for applying the First Law of Thermodynamics correctly.

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