Question

(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

The first law of thermodynamics is represented by the equation \(\Delta U = q - w\), where \(\Delta U\) is the change in internal energy, \(q\) is the heat added to the system, and \(w\) is the work done by the system. Heat and work will both be negative numbers when heat is flowing out of the system (exothermic process) and work is being done on the system, typically during compression.

Step-by-step solution

First Law of Thermodynamics Equation

The first law of thermodynamics states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. Mathematically, this can be expressed as: \[ \Delta U = q - w \] Where, \(\Delta U\) = change in internal energy, \(q\) = heat added to the system, and \(w\) = work done by the system. #Step 2: When will heat and work be negative numbers?#

Conditions for Negative Heat and Work

Let's consider the conditions under which \(q\) and \(w\) will be negative numbers. (a) Heat (q) will be negative when heat flows out of the system. This is called an exothermic process. (b) Work (w) will be negative when work is done on the system. This typically occurs when the system is compressed. So, heat and work will both be negative numbers when heat is flowing out of the system (exothermic process) and work is being done on the system.