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Chapter 5: Problem 26

(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?

Short Answer

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(a) The first law of thermodynamics equation is \(\Delta U = q - w\). (b) The conditions for negative \(q\) and \(w\) are: - \(q < 0\): Heat is released (exothermic process) - \(w < 0\): Compression work (work done on the system)

Step by step solution

01

(a) Write the first law of thermodynamics equation

To write the equation that represents the first law of thermodynamics, we will use the standard symbols: \(\Delta U\) for the change in internal energy, \(q\) for the heat added to the system, and \(w\) for the work done by the system. The equation is: \[\Delta U = q - w\]
02

(b) Determine the conditions for negative \(q\) and \(w\)

In the equation \(\Delta U = q - w\), \(q\) will be negative when heat is released by the system, and \(w\) will be negative when work is done on the system. 1. Heat (\(q\)) is negative when energy is being transferred from the system to the surroundings, which means the system is losing heat to the surroundings. This is called the exothermic process. 2. Work (\(w\)) is negative when the surroundings exert a force on the system, causing the system to compress or the external pressure to do work on the system. This is called compression work. In summary, the conditions for negative \(q\) and \(w\) are: - \(q < 0\): Heat is released (exothermic process) - \(w < 0\): Compression work (work done on the system)

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